cirx  OF 
Professor 

John  S.    Tatlo 


I 


^u 


essor 

f.-. .-   4-  T    , 


5.  •••* 

C*«  •         c*C  c 


•  •      •  • 

t>  ace  • 

•  •  •  •  • 


I  c  • 


•  •  •  • 


SECOND    EDITION 


A  COMPLETE  SYSTEM 

OF 

HARMONY 


BY 


H.    E.    PARKHURST 


Containing  a  thorough  practical  treatment  of  all  chord-formations 
and  connections,  an  exhaustive  analysis  of  suspension  and 
other  auxiliary  effects,  and  a  comprehensive  discus- 
sion of  organ-point,  modulation  and  cadence, 
with   exercises  therein  ;  constituting  a 
full  preparation  for  Counterpoint. 


CARL  FISCHER,  PUBLISHER 

COOPER  SQUARE 
NEW  YORK 


iRARY 


o: 


Bt. 


_y 


Copyright  1908 

By 

CARL,  FISCHER  —  NEW  YORK 

International  Copyright  Secured 


/ 


JT    ^  ^jCC^€^^ 


CONTENTS, 


INTRODUCTION— Definitions 5 

Part  I. 
THE  FUNDAMENTAL  CHORDS. 


PAGE 


CHAPTER  I.        —The  Common  Chord 14 

CHAPTER  II.      —The  Secondary  Common  Chords 23 

CHAPTER  III.    —The  Minor  Scale  and  its  Triads 35 

CHAPTER  IV.    —The  Inversions  of  the  Common  Chord ....     45 

CHAPTER  V.      —The  Chord  of  the  Seventh 58 

CHAPTER  VI.    —The  Inversions   of   the  Dominant-Seventh 

Chord 65 

CHAPTER  VII.  —Close  and  Open  Position— Concealed  Fifths 

and  Octaves  —  Score  —  Cross- Relation 

— Sig-ht-reading  71 

CHAPTER  VIII.— Secondary  Seventh  Chords 88 

CHAPTER  IX.    —Inversions  of  Secondary  Seventh  Chords..  100 
CHAPTER  X.      —Seventh  Chords  Followed  by  Various  Re- 
solving Chords 104 

CHAPTER  XI.    —Exceptional  Modifications  in  the  Resolu- 
tion of  the  Seventh 108 

CHAPTER  XII.  —Altered  Chords 112 


Part  II. 
THE  AUXILIARY  CHORDS. 

CHAPTER  XIII.    —Suspension 128 

CHAPTER  XIV.    — Suspension  (concluded) — Anticipation — 

Syncopation 161 

CHAPTER  XV.      — Auxiliar  Tones 178 

CHAPTER  XVI.    —Rhythm— Primary,  Secondary  and  Auxi- 
liary Chords 194 

CHAPTER  XVII.  —The  Organ-Point 209 

CHAPTER  XVIII.— Modulation 219 

CHAPTER  XIX.    —Modulation     (concluded)  —  Chromatic 

Chords 236 

CHAPTER  XX.      —Cadences 242 

APPENDIX 252 

ivi206S63 


THK   DISTINCTIVE    FEATURES   OF   THIS   WORK    MAY   BE 
BRIEFLY    STATED. 


^■■P^HE  extended  and  systematized  treatment  of  the  Auxiliary 
/  1  Chords  is  prompted  by  the  conviction  that  a  modification 
^^^  is  sorely  needed  in  the  prevalent  method  of  harmonic 
teaching.  The  vast  majority  of  pupils,  leaving  Harmony 
with  little  or  no  drill  except  in  the  Fundamental  Chords,  plunge 
into  Counterpoint  and  Fugue  so  ill-prepared  for  the  require- 
ments of  these  advanced  studies,  that  their  most  laborious  efforts 
produce  only  painfully  unmusical  results.  At  present,  the  pupil 
sees  little  relation  between  his  chords  of  Harmon}-  and  the  chord- 
formations  of  actual  composition,  and  this  is  because  he  has  not  been 
taught  how  to  elaborate  his  fundamental  harmonies  with  auxiliary 
effects. 

The  principles  of  Modulation  have  been  presented  in  a  manner 
that  will,  it  is  hoped,  make  what  is  the  most  subtle  feature  of  com- 
position more  intelligible  and  attractive  to  the  pupil .  If  in  many 
text -books  the  true  philosophy  of  the  matter  has  not  been  miscon- 
ceived, it  has  certainly  been  strangely  misrepresented. 

Organ-point  is  generally  treated  in  so  superficial  a  manner,  that 
it  will  be  a  surprise  to  some  that  it  can  be  reduced  to  a  scientific 
system  which  shows  it  to  be  amenable  to  the  laws  of  Harmony, 
instead  of  being  an  authorized  license  to  violate  almost  all  the  pre- 
established  requirements  of  chord  progression.  Its  treatment  in 
this  work  is  the  first  attempt,  so  far  as  the  author  is  aware,  to  bring 
under  distinct  rules  this  effective  species  of  composition,  and  to 
.afiPord  to  the  pupil  a  method  of  learning  it. 


Special  emphasis,  b}^  means  of  special  exercises,  has  been  put 
npon  the  need  of  distinct  knowledge  of  the  effect  of  chords  without 
playing  them., — a  matter  strangely  ignored  in  some  text  books — the 
neglect  of  which  makes  all  study  of  musical  theory  absolutely 
profitless. 

As  a  means  of  bringing  the  contents  of  each  chapter  under 
distinct  review,  a  Summary  is  appended,  both  for  self-examination 
and  for  the  teacher's  use. 

Insufficient  drill  in  elementary  harmony — which,  as  Rhein- 
berger  was  wont  to  remark,  is  nine- tenths  of  the  whole  art— in  na 
small  degree  accounts  for  the  comparative  shallowness  of  modern 
composition;  and  the  very  best  preparation  for  expressing  one's 
individuality  in  musical  thought  is  rigid  discipline  in  those  funda- 
mental harmonic  principles  that  yield  to  no  passing  fashion,  but 
underlie  all  thoughtful  music,  be  it  classical  or  ultra-modern . 

THE  AUTHOR 

New  York,  July  31^  l9Gi. 


INTRODUCTION. 


Definitions. 

Kvery  concussion  of  air  affecting  the  ear  produces  sound. 

Sounds  are  of  two  distinct  kinds,  viz.,  noise  and  tone. 

Single  impacts  upon  the  ear,  or  a  series  of  impacts  following 
more  or  less  rapidly,  but  irregularly,  produce  noise;  as,  a  single  clap 
of  thunder,  or  a  reverberation  of  thunder,  which  is  produced  by  an 
irregular  succession  of  echoes. 

A  succession  of  impacts  upon  the  ear,  following  rapidly  and 
equidistant,  produces  tone;  as,  the  vibrations  of  a  violin  string. 
Rapidity  and  equidistance  of  vibrations  are  the  conditions  of  tone; 
i.  e.,  musical  sound.  The  pitch  of  the  tone  varies  with  the  rapidity, 
the  lowest  distinguishable  tone  having  about  i6  vibrations  in  a  sec- 
ond, and  the  highest,  from  16,000  to  33,000. 

A  single  tone  is  musical,  but  it  is  not  music;  it  is  the  basal  atom 
of  music. 

Music  is  the  intelligent  combination  of  tones.  Two  sorts  of  com- 
bination are  possible,  viz.,  successive  and  simultaneous. 

Melody.  The  musical  sense  of  successive  single  tones  is  called 
melody. 

Beethoven^ 


Andante 


Harmony.     The  musical  sense  of  simultaneous  tones  is  called 
har)no)i\'. 


I 


xe: 


-o- 


This  latter  combination  constitutes  a  chord.  Radically  distinct,  each 
is  the  necessary  supplement  of  the  other.  They  are  the  soul  and 
body  of  music.  Melody  without  harmony  is  disembodied  spirit. 
Harmony  without  melody  is  lifeless. 


6  PARKHURST  HARMONY, 

Simultaneous  tones,  producing  an  agreeable  effect,  constitute  a 
concord  or  consonance ;  producing-  a  disagreeable  effect,  a  discord  or 
dissonance.  Concords  are  not  all  equally  agreeable,  neither  are  dis- 
cords all  equally  disagreeable.  (The  list  of  concords — or  con- 
sonances— and  discords — or  dissonances — will  be  given  later). 

It  may  seem  incongruous  that  any  effect,  in  itself  disagreeable, 
should  be  admissible  in  music ;  it  is  equally  incongruous  that  salt,  by 
itself  utterly  distasteful,  should  be  the  necessary  ingredient  of  all 
food.  Discordance  is  simply  salt  for  seasoning.  Harmony  would  be 
insipid  without  it. 

If  any  one  chooses  to  apply  the  term  dissonance  to  those  harsh 
effects  which  are  admissible  in  music,  and  the  term  discord  to  those 
effects  which  are  too  harsh  to  be  serviceable,  there  is  no  law  against 
such  a  classification,  nor  is  there  any  authority  for  it,  inasmuch  as 
discord  (dis-corda)  and  dissonance  (dis-sonans)  from  their  etymo- 
logy have  identically  the  same  meaning.  We  shall  see,  later,  how  the 
discord  is  softened  or  concealed  to  the  degree  of  being  palatable. 

Harmony.  This  word,  already  partially  defined,  in  its  relation  to 
melody,  is  used  in  three  senses,  closely  allied,  yet  quite  distinct.  In 
the  first  and  most  popular  sense,  harmony  is  equivalent  to  concord, — 
harmonious  means  the  perfectly  agreeable,  and,  the  inharmonious 
involves  more  or  less  of  discordance.  But  the  musical  sense  of 
simultaneous  sounds  does  not  limit  us  to  pure  concords.  There  are 
many  chords,  tinged  more  or  less  with  discordance,  whose  use  greatly 
enhances  the  aggregate  effect  of  music ;  and  in  a  technical  sense  all 
combinations  of  tones,  purely  concordant  or  not,  which  are  service- 
able in  the  expression  of  musical  sense,  are  termed  harmonies:  as 
when  we  speak  of  the  ''harmonies"  of  a  composition,  meaning  the 
chords.  In  the  third  use  of  the  word,  Harmony  constitutes  the  first 
grand  division  of  Musical  Theory,  and  is  the  subject  of  the  present 
work.  Used  in  this  sense,  Harmony  is  the  science  of  fundamental 
and  auxiliary  chords  in  their  individual  construction  and  their  proper 
connection  one  with  another.  More  briefly  expressed,  it  is  the 
science  of  the  construction  and  connection  of  chords. 

In  its  three  senses 

Harmony  means  — concord. 
"      —chord. 
**  **      — the  science  of  chords. 

This  is  the  scope  of  our  present  work,  the  foundation  of  all  further 
theoretical  study.  It  will  be  well  for  the  pupil  to  understand  the 
nature  and  the  limits  of  his  present  undertaking,  that  at  its  conclu- 
sion he  may  not  be  disappointed  because  he  has  not  learned  what 


INTRODUCTION.  7 

lies  altogether  beyond  the  province  of  Harmony.  Tones  are  to  the 
composer  what  colors  are  to  the  painter,  and  he  must  first  learn  the 
colors,  their  mixture  in  single  chords,  their  combination  in  a  flow 
of  harmonies,  before  he  can  expect  any  results  that  deserve  the 
name  of  original  composition. 

Harmony,  as  the  science  of  chords,  is  often  called  the  grammar 
of  music.  But  it  is  more.  It  is  also  the  spelling  book.  The  several 
tones  represent  the  letters  of  the  musical  language,  their  combination 
in  chords  spells  out  the  zvords,  and  lastly  the  proper  connection  of 
the  chords  is  analogous  to  the  grammatical  construction  of  language. 
We  shall  first  have  to  learn  how  chords  are  formed,  i.  e.,  spelled,  be- 
fore we  can  properly  connect  them. 

In  the  definition  of  melody  and  harmony  it  became  evident  how 
meaningless  the  latter  is,  except  as  it  is  animated  by  the  former.  But 
it  is  to  be  observed  that  the  part  or  voice  that  furnishes  the  melody 
(usually  the  highest  part)  is  also  a  constituent  part  of  the  harmony; 
that  is,  the  tones  of  the  melody  are  at  the  same  time  elements  of  the 
successive  chords  underlying  the  melody ;  ( for  example,  the  soprano 
part  of  "Old  Hundred").  But  our  present  purpose  will  be  best  at- 
tained by  subordinating,  for  the  time  being,  the  melodic  quality  of 
the  upper  part  to  its  harmonic  character,  so  that  throughout  Har- 
mony, and  especially  at  the  first,  the  exercises  will  have  scarcely 
more  than  a  tinge  of  melodic  effect.  But  while  the  highest  tone  of 
each  chord  will  be  treated  primarily  as  an  element  of  the  harmony, 
the  pupil  is  still  to  give  to  the  highest  part  as  much  of  the  melodic 
quality  as  is  consistent  with  the  harmonic  requirements.  A  more 
free,  melodic  character  in  the  highest  part  will  follow  in  due  time, 
and  the  pupil  will  then  have  acquired  a  correct  treatment  of  the 
underlying  harmony. 

Intervals. 

An  interval,  in  music,  is  the  distance  hetwef>n  tw^  toneis.  The 
distance  from  any  tone  to  the  next  clearly  individual  tone  above  or 
below  is  called  a^emjtgne,  or  a  half-step ;  as,  from  C  to  Db.  E  to  F. 


$ 


^ 


jy 


A  musical  sound  can  indeed  be  produced  between  C  and  Db,  but,  as 
relative  to  these,  it  has  no  individuality ;  it  will  be  regarded,  not  as  a 
distinctive  tone,  but  as  a  defective  C  (being  too  high)  or  a  defective 
Db  (being  too  low). 


PARKHURST  HARMONY. 


(Note.  It  is  doubtful  whether  the  distance  between  two  clearly 
distinct  tones  has  ever  been  less  than  what  is  now  called  a  semitone. 
It  is  true,  that  in  the  Indian  music  we  find  the  octave  divided  into  22 
parts,  instead  of  12,  as  with  us,  by  which  they  obtain  a  quarter-tone 
instead  of  a  semitone  as  their  smallest  distance.  But  this  subdivision 
is  purely  theoretical,  and  does  not  exist  in  their  practice.) 

The  sum  of  two  semitones,  as  from  C  to  D,  or  from  E  to  F#, 
is  called  a  tone  or  a  step.  This  word  tone  thus  has  two  meanings: 
first,  that  of  musical  sound ;  secondly,  that  of  distance,  as  the  sum  of 
two  semitones.  This  use  of  the  word  as  a  measure  of  distance  is 
authorized  by  the  word  diatonic,  in  which  tone  (from  the  Greeks 
tonos),  has  the  same  significance.  This  double  sense  of  the  word 
will  not  be  found  to  involve  any  ambiguity. 

For  the  sake  of  uniformity,  all  intervals  are  reckoned  from  the 
lower  tone  upward,  unless  otherwise  expressly  stated.  An  interval  is 
reckoned  on  the  staff  by  counting  the  intervening  lines  and  spaces 
between  the  two  notes,  and  adding  those  on  which  the  notes  them- 
selves are  placed.  Thus  from  C  to  D  is  called  an  interval  of  a  second, 
from  C  to  E  a  third,  etc.,  as  follows : — 

Second.    Third.       Fourth.     Fifth.       Sixth.    Seventh.    Eighth. 


i 


-o^ 


IE 


33: 


XH 


"O" 


The  interval  has  the  same  name  even  if  either  of  the  tones  be 
raised  or  lowered  by  an  accidental,  thus: 


^ 


Seconds 


Thirds. 


Sixths. 


XE 


XE 


323X 


-^ 


-O^ 


IX 


-o- 


-e^ 


♦V 


4^ 


Accordingly,  intervals  of  the  same  name  are  not  always  of  the 
same  size;  and  to  express  the  intervals  precisely  they  must  have  a 
further  designation.  The  following  list  presents  two  sizes  of  each 
interval  within  the  limits  of  an  octave,  beginning  with  C : 

Seconds.  Thirds.  Fourths.  Fifths, 

minor,  major,  minor,    major,    perfect. augmented. perfect. augmented. 


i 


m 


r€T 


I 


Sixths 


^ 


w^ 


XE 


XH 


-€>- 


1 


minor. 


XE 


major. 


XE 


Sevenths, 
mmor.  major. 


Octave. 

perfect. 


INTRODUCTION.  9 

The  two  sizes  differ  in  each  case  by  a  semitone,  and  in  all  but  two 
cases  the  less  is  called  minor,  the  greater,  major.  The  two  excep- 
tions are  in  the  fourths  and  fifths,  where  the  terms  perfect  2ind  aug- 
mented are  used. 

There  is  one  more  augmented  interval  which  must  be  noticed; 
viz.,  the  augmented  second,  thus: 

Augmented  Seconds. 


^^^^Inrl^^J^P 


This  peculiar  interval  will  demand  our  attention  later. 

Another  important  interval  is  a  species  of  a  fifth,  which  is,  how- 
ever, a  semitone  less  than  the  perfect  iifth  and  is  called  the  dimin- 
ished fifth ,  thus : 


Diminished  Fifths. 


I 


o^ 


TSl 


W 


lOE 


Tones  identically  situated  are  said  to  be  in  unison. 


i 


Unisons. 


I^^o    |g*M» 


^»^ 


From  any  letter  to  the  same  letter  above  is  an  octave  or  eighths 
From  C  to  the  second  D  above  is  strictly  a  ninth,  but  there  is  such 
identity  in  the  quality  of  every  tone  and  that  of  its  octave  that  for  all 
present  harmonic  purposes  we  can  reckon  this  interval  as  a  second; 
similarly  an  interval  of  a  tenth  is  regarded  as  ^a  third,  and  so  on; 
and  however  many  octaves  intervene,  the  interval  is  reckoned  as^ 
being  within  the  limits  of  one  octave;  thus: 


_ti. 


JCL        ^ 


33: 


XE 


-cv 


-o- 


Second.  Third.  Fourth.Fifth.Sixth.Seventh.Eighth, 


Third, 


Fifth. 


Sixth 

etc. 


^^ 


-^ 


The  following  is  a  list  of  the  most  commonly  occurring  intervals,  and 
the  only  ones  with  which  the  pupil  need  concern  himself  at  present; 


YO 


PARKHURST  HARMONY. 


$ 


Unison.      Seconds. 


Thirds. 


Fourths. 


^o  '.^:tt^ir4^o  "im.  '^8,  "ji;;-  't,^ 


ix 


Fifths, 
diminished,  perfect,  augmented^  minor. 


Sixths. 

major,     augmented^ 


trrr 


jce 


xn 


i 


Sevenths.  Octave, 

diminished,  minor,     major,     perfect. 


^^3 


■r 


1F 


* 


jce: 


(For  a  full  list  of  all  intervals  see  Appendix  (A)). 

A  word  must  be  said  concerning  the  proper  manner  of  learning 
the  above  intervals.  An  interval  has  not  been  learned  when  the  pupil 
is  merely  able  to  tell  how  many  tones  and  semitones  are  comprised 
within  the  distance;  as,  for  example,  that  there  are  two  semitones 
in  a  major  second,  two  whole  tones  in  a  major  third,  etc. ;  this  is 
mathematically  correct,  but  an  utterly  inadequate  knowledge  of  the 

intervals.    Again,  to  see  in  the  interval  from  C  to  G, 

merely  a  fifth,  from  the  bare  computation  of  lines  and  spaces,  with- 
out associating  with  this  interval  the  quality  of  a  perfect  fifth,  which 
distinguishes  it  from  every  other  possible  interval — such  a  process 
misses  entirely  the  recognition  of  the  most  interesting  aspect  of  the 
interval,  its  real  individuality  and  character.  Thus  it  means  nothing 
to  know  that  a  major  third  is  greater  by  a  semitone  than  a  minor 
third.  The  real  difference  of  these  two  intervals  is  not  in  the  size, 
but  in  the  quality  of  the  two  kinds  of  thirds.     Play  the  major  third 


^^P 


then  depress  the  E  to  Eb 


^ 


notice  the  strong, 


vigorous,  masculine  quality  of  the  major,  and  the  weak,  almost  femi- 
nine quality  of  the  minor  ;  compare  also  the  following : 


$ 


.  »  |ffU||»|l;« 


By  discovering  these  diverse  qualities  of  the  intervals,  one  comes 
truly  to  know  them,  and  only  such  knowledge  can  insure  success  in 
the  study  of  Harmony,  for  it  is  a  constant  study  of  combinations  of 
tones.     Intervals  can  be  computed,  with  absolutely  no  sense  of  their 


INTRODUCTION.  U 

effect,  and  a  large  proportion  of  Harmony  students  are  simply 
computing  their  intervals !  The  result  is,  that  while  the  exercises 
are  written  with  some  degree  of  mechanical  correctness,  they  find 
on  completing  Harmony  that  they  are  confronted  by  an  impenetrable 
barrier,  forbidding  any  further  progress,  li  they  do  not  then  give 
up  the  study  in  disgust,  they  proceed  to  "review"  by  precisely  the 
same  process ! 

It  carniot  be  too  strenuously  urged  upon  the  pupil  to  begin  this 
work  ^ith  the  resolve  to  know  the  effect  of  every  combination  he 
writes,  and  to  associate  it  with  the  writing  every  time;  that  is,  to 
imagine  the  effect  constantly,  smd  to  play  the  exercise  only  after  he 
has  as  clear  an  idea  of  it  as  possible,  and  thus  correct  his  idea 
of  the  effect  by  the  actual  sound.  In  this  way  the  study  of  "Theory" 
will  increase,  rather  than  diminish,  in  interest.  To  this  end  let  the 
pupil  resolve  to  become  as  independent  of  the  piano  as  possible,  in 
getting  a  clear  idea  of  his  chords. 

At  each  lesson  the  teacher  should  play  the  different  intervals, 
major  and  minor,  and  have  the  pupil  name  them,  so  that  he  will 
know  them  by  sound,  and  not  merely  by  sight. 

As  an  exercise  in  the  study  of  intervals,  let  the  pupil  analyse  the 
following  series  of  tones,  ascertaining  the  interval  from  the  first  to 
each  succeeding,  then  from  the  second  to  each  succeeding,  then  from 
the  third,  etc.,  always  reckoning  a  ninth  as  a  second,  as  before  ex- 
plained.   This  will  bring  to  view  all  of  the  usual  intervals. 


11    o     ^ 


ti    o 


ft    Q 


—  — xr^eK  o    o 
It    o     "    ^    "^ 


if     o 


•  1      o 


After  this  analysis,  go  through  the  series  again,  finding  all  the 
minor  seconds,  major  seconds,  minor  thirds,  major  thirds,  perfect 
fourths,  etc.,  throiigh  the  list  of  intervals. 

The  Scale. 

Scala,  from  which  the  word  scale  is  derived,  means  a  ladder;  and 
in  its  application  to  music  it  means,  literally,  any  ascending  or  de- 
scending series  of  tones  at  equal  or  nearly  equal  intervals  from  each 
other.  When  the  intervals  exceed  that  of  a  second,  the  series  of 
tones  is  called  an  arpeggio,  from  arpa,  meaning  a  harp;  an  arpeggio 
being  such  a  succession  of  tones  as  is  most  characteristic  of  the  harp. 


42 


PARKHURST  HARMONY. 


.  The  scale,  in  its  usual  sense,  means  a  series  of  eight  tones,  with 
intervals  of  a  major  or  minor  second  (i.  e.,  tones  or  semitones)  be- 
tween adjacent  tones.  For  the  most  part  the  interval  between  adja- 
cent tones  is  a  major  second,  that  is,  a,  whole  tone,  hence  called  the 
diatonic  scale  ( from  the  Greek  words,  dia,  and  tonos,  by  means  of, 
or  through,  whole  tones)  in  which  this  interval  predominates. 

The    Major   and   Minor   Diatonic    Scales. 

The  diatonic  scale  is  of  two  sorts,  according  to  the  location  of 
the  semitones.  These  two  sorts  are  called  the  major  and  the  minor. 
In  the  major  diatonic  scale,  with  which  we  have  principally  to  do,  the 
semitones  occur  between  the  third  and  fourth,  and  between  the 
seventh  and  eighth  tones,  thus: 

1       1      i/a — 4, — 4 4 — i/g. 


I 


jDl 


XE 


O 

'This  is  the  invariable  construction  of  the  major  diatonic  scale.  To 
become  familiar  with  its  formation,  let  the  pupil  construct  the  same 
scale,  beginning  upon  the  following  letters  of  the  staff,  viz.:  G,  D, 
A,  E,  F,  Bb,  Kb,  Ab,  using  sharps  or  ^ats  as  may  be  necessary  to 
preserve  the  correct  intervals. 

The  formation  of  the  minor  diatonic  scale,  and  the  reason  for  the 
use  of  the  terms  major  and  minor,  will  be  given  in  a  subseauent 
chapter. 

The  Chromatic  Scale. 

This  is  the  series  of  successive  semitones  or  half -steps: 


jf4iO"ol^o«t|;<fi=fe; 


.tf^o<tooo|to0<|oojt. 


•^obool^o^ 


melody  and  harmony  do  not  move  in  this  scale,  but  only  in  the  dia- 
tonic scale ;  therefore  it  does  not  serve  practically  as  a  scale,  like  tlie 
major  and  minor  diatonic  scales ;  it  is  rather  the  filling  out  of  all  the 
half-steps  in  any  diatonic  scale  that  happens  to  be  used,  has  no 
signature  of  its  own,  occurs  only  exceptionally,  and  almost  exclu- 
sively in  short  fragments  in  elaborated  music,  thns: 


'i'l^wihi^ 


niHii 


M 


INTRODUCTION. 


13 


Such  passages  as  the  above,  and  in  general  any  passage,  in  which 
an  unusual  number  of  accidentals  are  used  in  one  or  more  voices  to 
embellish  the  single  harmonies  of  the  scale,  are  called  chromatic. 


^ 


m 


*i 


t=i 


*  -^  -^- 


t_-  f     Y 


^ 


\^r  ^r  \^r  ^ 


g 


XT 


It  is  expected  that  the  student  of  Harmony  will  have,  at  this  point, 
not  only  a  clear  idea  of  the  major  diatonic  scale,  so  that  he  can  con- 
struct the  same,  beginning  with  any  of  the  above-named  letters, 
either  on  the  staff  or  on  the  pianoforte,  but  also  a  fair  knowledge 
of  the  most  commonly  used  intervals,  as  regards  their  computation 
and  effect.  With  this  preliminary  knowledge  he  will  be  prepared  to 
enter  upon  the  work  of  the  following  chapters. 

Summary. 

Sound. — Distinction  between  noise  and  tone. — The  two  condi- 
tions necessary  for  tone. — What  determines  the  pitch. — About  how 
many  vibrations  in  the  lowest  and  the  highest  tones. — Define  music. 
— Define  melody. — Define  harmony. — Distinction  of  concord  and 
discord. — Three  senses  of  the  term  Harmony. — Define  interval. — De- 
fine semitone  and  tone. — How  intervals  are  reckoned. — Difference  in 
size  between  major  and  minor  intervals. — Illustrate  two  sizes  of  each 
interval,  from  a  second  up  to  a  seventh. — Define  augmented  second, 
also  diminished  fifth. — Define  miison  and  octave. — How  intervals 
greater  than  an  octave  are  reckoned. — Every  interval  to  be  known  by 
its  quality  or  effect,  and  not  merely  by  its  computed  size. — Indepen- 
dence of  the  piano  to  be  aimed  at. — Meaning  of  scale  and  arpeggio. 
— Derivation  of  diatonic. — Formation  of  major  diatonic  scale. — The 
chromatic  scale,  and  how  used. 

The  "Summary"  at  the  end  of  each  chapter  affords  to  the  pupil 
the  means  of  examining  himself  in  the  contents  of  each  chapter. 


HARMONY. 

The  term  ''Harmony"  has  already  been  defined  as  the  Science  of 
the  construction  and  connection  of  fundamental  and  auxiliary  chords. 

This  definition  suggests  the  proper  division  of  the  present  work 
into  two  parts. 


J4  PARKHURST  HARMONY, 

PART  I. 
THE  FUNDAMENTAL  CHORDS. 

The  first  and  most  general  analysis  of  the  fundamental  chords 
classifies  them  into  two  sorts ;  first,  those  which  show  no  definite, 
inherent  connection  with  other  chords,  and  thus  do  not  determine  in 
any  degree  what  chord  shall  follow  them.  These  are  called  the  in- 
dependent  chords.  Secondly,  those  which  do  show  an  inherent  con- 
nection with  other  chords,  and  thus  to  a  degree  determine  what  chbfd 
"^hall  follow  them.    Thisse  are  called  the  dependent  chords. 

To  the  first  class  belong  in  general  the  ^'common  chords,"  which 
are  the  first  to  be  explained. 

CHAPTER   I. 

The  Common   Chord. 

The  simplest,  most  elementary  combination  of  tones,  which  serves 
as  the  basal  combination  underlying  all  harmonic  formations,  is 
the  common  triad.  Triad  means  three-foldness,  whether  of  tones  or 
of  any  other  object.  Any  three  tones  constitute  a  triad.  But  that  com- 
bination which  is  specifically  called  ''the  common  triad"  consists  of 
any  tone  of  a  diatonic  scale,  to  which  is  added  its  third,  and  its  Hfth 
in  the  scale. 


^ 


The  triad  is  named  from  its  lowest  letter,  which  is  also  called  the 
root  or  fundamental  of  the  triad.    Thus  the  above  is  the  triad  of  C. 

As  there  are  seven  distinct  tones  in  the  scale,  and  each  can  be  the 
root  of  a  triad,  we  can  have  seven  distinct  triads,  as  follows : 


As  the  greater  part  of  all  fundamental  harmonies  are  expressed  in 
the  above  series,  it  is  desirable  to  examine  them  closely,  and  learn 
their  similarities  and  their  diflferences. 

(Let  the  pupil  first  play  them  carefully,  one  by  one,  and  notice 
their  effect ;  then  let  him  begin  the  series  again,  and  recall  the  effect, 
as  nearly  as  possible,  of  each  in  succession.  By  this  discipline  he  will 
acquire  a  clear  idea  of  the  musical  sense  of  a  chord  without  the  neces- 
sity of  playing  it.) 


CHAPTER  L  15 

The  more  carefully  they  are  compared,  the  more  distinct  is  the 
effect  of  each  from  that  of  all  the  others,  while  in  them  all  is  also 
evident  a  similarity.  Each  is  similar  to,  and  each  is  distinct  from,  all 
the  rest.  The  similarity  is  due  to  a  single  cause,  viz.,  that  they  are 
all  formed  in  the  same  way,  by  adding  to  each  root  the  third  and 
fifth  above  it ;  and  all  thirds  have  a  similarity  to  each  other,  and 
?.ho  all  fifths.  This  then  accents  for  the  manifest  uniformity  in  the 
effect  of  all  the  triads. 

Thit  variety  in  the  triads  is  due  to  two  causes ;  first,  while  there 
is  a  certain  quality  of  effect  common  to  all  triads,  there  is  also,  as 
we  have  already  seen,  a  marked  difference  between  a  major  and  a 
minor  third ;  and  some  of  the  triads  have  major,  and  others  have 
minor  thirds.  (Let  the  pupil  classify  the  triads  according  to  the  two 
kinds  of  thirds,  and  play  each  group  by  itself.)  Again,  while  six  of 
them  have  perfect  fifths,  one  (on  the  7th  of  the  scale),  has  a  dimin- 
ished fifth.  The  diiferent  kinds  of  thirds  and  fifths  produce  in  part 
the  difference  in  effect.  Secondly,  a  little  examination  of  the  scale 
shows  that  it  is  not  simply  a  series  of  tones  differing  merely  in  pitch 
(which  is  simply  a  mechanical  difference),  but  that  these  tones  have, 
in  their  scale-relation  to  each  other,  distinct  individuality  of  char- 
acter. This  is  most  evident  in  the  case  of  the  first  tone,  the  keynote 
of  the  scale,  which  is  plainly  more  important  than  any  other.  By 
carefully  playing  the  scale,  one  learns  to  recognize  more  and  more 
the  distinctive  quality  of  each  tone.  The  seven  tones  of  the  scale 
may  be  compared  to  the  seven  primary  colors,  and  in  the  variety  of 
coloring  of  the  scale-tones  we  find  the  same  reason  for  the  diversity 
of  effect  in  the  triads.  The  pupil  can  well  afford  to  spend  a  little 
time  in  verifying  the  foregoing  statement,  as  his  interest  and  success 
in  the  subsequent  work  will  be  in  proportion  as  he  realizes  their 
force. 

Major  and  Minor  Triads. 

Triads  are  called  major  or  minor,  according  as  the  middle  tone 
is  a  major  or  minor  third  from  the  root.  (The  relation  of  the  middle 
tone  to  the  root  is  much  more  determinative  of  the  general  effect  of 
the  triad  than  is  the  relation  of  the  middle  to  the  upper  tone,  which 
is  therefore  left  out  of  the  account).  As  the  major  third  is  stronger 
than  the  minor,  the  major  triads  are  stronger  and  more  important 
than  the  minor  triads.    In  this  respect  the  three  following 


^^ 


16  PARKHURST  HARMONY. 

are  more  important  than  the  four  following : 


$ 


^ 


^ 


II    III    VI    VII 

Perfect  and  Diminished  Triads. 

As  regards  the  fifth  in  the  triad,  a  perfect  fifth  is  evidently 
stronger  than  a  diminished  fifth,  and  in  this  respect  we  have  six 
strong  triads  — 


4^11  yng» 


and  one  weak  one  — 


m 


(This  last  is  doubly  weak,  in  having  a  minor  third,  as  well  as  dimin- 
ished fifth). 

Triads  are  strong  and  important,  not  only  according  to  the 
strength  of  the  intervals  composing  them,  but  also  according  to  the 
strength  of  the  scale-tones  involved  in  them.  The  strongest  and  rul- 
ing tone  of  the  whole  scale  is  the  keynote,  which  is  also  called  The 
Tonic. 

The  next  strongest  tone  is  the  fifth.  This  is  the  dominating  tone 
of  the  scale,  next  to  the  Tonic,  and  is  characterized  by  the  name 
Dominant. 


I 


-t*- 


The  Tonic  and  the  Dominant  are  the  two  foundation  tones  of  all 
music.  It  is  the  great  importance  of  these  tones  which  to  a  large 
degree  causes  the  triads  founded  upon  them  to  be  the  most  important 
in  harmony. 


^^§ 


They  are  also  otherwise  strong  in  having  a  major  third  and  a 
perfect  fifth. 

Reckoning  upzvard  a  fifth  from  the  Tonic  (C)  we  reach  the 
Dominant  (G).    Reckoning  downward  a  fifth  from  the  Tonic  (C) 


'i 


CHAPTER  /. 


17 


we  reach  F, 


I 


JLi. 


XI 


or 


which  we  find  to  be  the  root  of  a  strong  triad  (major  third,  per- 
fect fifth),  and  having  moreover  the  Tonic  (C)  as  one  of  the  ele- 
ments of  the  triad. 

As  being  the  foundation  tone  of  so  important  a  chord,  rather  than 
by  virtue  of  its  own  distinctive  quaHty,  this  fifth  below  (F)  is  called 
the  SuBDOMiNANT,  i.e.,  the  wwrf^r-dominant,  ruling,  below  the 
Tonic,  somewhat  as  the  Dominant  rules  above.  \  According  to  the 
usual  method  of  reckoning  intervals  upward,  F  will  be  spoken  of  as 
the  Fourth  above  C,  and  the  significance  of  the  term  subdominant 
is  obscured.    But  from  the  foregoing  the  reason  for  the  term  is  plain. 

Primary  and  Secondary  Triads. 
The  triads  of  the  scale  are  classified  into  Primary  and  Secondary, 
according  to  their  importance.  The  primary  triads  are  those  of  the 
Tonic,  Dominant  and  Subdominant  (which  are  also  the  major 
triads).  The  Secondary  triads  comprise  all  the  remaining,  i.  e.,  on 
the  2d,  3rd,  6th  and  7th  degrees  of  the  scale  (which  are  also  the 
minor  triads). 


hn.Al  5  '' 


I  II  "^  ^^  '  VI  VII 
Our  exercises  will  begin  with  the  use  of  the  Primary  triads.  But 
we  must  first  speak  of  the  number  of  tones  or  parts  that  constitute 
our  fundamental  chords.  As  the  elementary  triad  consists  of  three 
distinct  tones,  it  might  be  supposed  that  our  elementary  harmonies 
would  be  composed  in  three  parts.  But  the  number  of  parts  is  de- 
pendent upon  other  principles,  which  are  more  fully  explained  in  the 
Appendix  (B).  It  will  then  suffice  here  to  say  that  fundamental 
harmonies  are  properly  considered  as  being  four-toned,  or  four- 
z'oiced.  It  is  therefore  evident  that  in  the  use  of  the  most  elemen- 
tary combination,  the  triad,  one  of  the  tones  must  be  doubled.  We 
have  our  choice  of  doubling  either  the  root-tone,  the  third,  orJiie 
fifth,  thus: 


i 


^douMed^'  ^^^^^  doubled. fifth  doubled. 


^.r 

^ 


» 


33: 


-♦♦- 


g 


3CE 


xs: 


-AX 


=S= 


g 


XH 


\6 


PARKHURST  HARMONY. 


The  only  law  to  determine  which  it  shall  be  is  the  law  of  effec- 
tiveness, and  experience  proves  it  to  be  the  best  in  general  to  double 
the  root-tone. 

Constructing  a    four-toned   harmony   of   the   C   triad   we  have 


^^ 


Variety  in  this  chord,  without  any  essential  difference,  can  be 
secured  by  arranging  the  three  upper  tones  of  the  harmony  in 
different  order.  All  possible  combinations  of  this  sort  will  still 
give  the  same  common  chord  of  C ,  thus : 


[#^=-1 



-H— 

f=\ 

~rs — 

<> 

— ¥T 

4> 

^ 

-O 

L-o — 1 

4> 

— C^ 

-o- 

y    «» 

4> 

_JJ 

4> 

4> 

i> 

4> 

4> 

«V 

2V 

Such  a  difference  as  is  indicated  above  is  called  a  difference  of 
position.  The  utility  of  such  variety  of  position  will  be  seen  later. 
The  above  example  illustrates  what  is  possible  in  the  case  of  every 
common  chord.  Let  the  pupil  write  a  similar  variety  of  position  of 
the  following  chords : 


-o- 


-o^ 


XE 


-€>■ 


Chord-Connection. 

The  chords  of  C,  F,  D  and  G  are  each  written  correctly  in  the 
following : 


i 


^^ 


^ 


g 


w 


t 


ZE 


but  if  played  in  succession,  it  is  evident  there  is  no  proper  connection 
between  them,  no  natural  flow  of  the  harmony ;  and  our  object  is,  to 
learn  not  only  the  correct  formation  of  each  chord,  but  also  their 
proper  connection  one  with  another. 

For  ease  of  expression,  in  referring  to  the  several  tones  of  a 
chord,  we  shall  apply  to  them  the  same  names  as  are  used  in  vocal 


CHAPTER  I. 


19 


harmony,  viz :  soprano,  alto,  tenor  and  bass.  This  does  not,  how- 
ever, involve  the  necessity  of  considering  the  parts  as  performed  by 
the  voice,  rather  than  by  any  other  instrument.  Of  these  parts  the 
highest  and  lowest  are  called  the  outer;  the  others,  the  inner  or 
middle  voices. 

Varieties  of  Motion. 

Before  giving  the  rules  for  the  proper  connection  of  chords  we 
must  speak  of  the  different  kinds  of  motion  of  the  several  parts  or 
voices,  relatively  to  each  other. 

There  are  three  kinds  of  motion  possible  : 

Parallel, 

Voices  moving  in  same  direction  simultaneously. 


I 


^^ 


rf=^ 


xn 


Contrary, 

Voices  moving  in  opposite  direction  simultaneously, 


$ 


Uy^ 


iTTf 


3X 


Oblique, 

One  voice  stationary,  another  moving  in  either  direction. 


# 


th 


rff 


XE 


^^1[JJ|» 


Of  these  sorts  of  motion,  contrary  is  to  be  preferred.  (For  the 
explanation  see  Appendix  (C)  ).  The  two  parts  most  conspicuous  in 
their  relation  to  each  other  are  the  outer  parts ;  contrary  motion  is 
therefore  to  be  sought  in  these  parts,  where  it  is  not  inconsistent  with 
other  requirements. 

Allowable  Progression  of  Each  Voice. 

Our  present  harmonies  and  their  progressions  are  the  funda- 
mental ones.  Therefore  the  movement  of  each  voice  must  be  simple. 
Effect,  in  its  usual  sense,  must  be  sacrificed  to  simplicity.  In  general 
the  less  movement  the  better,  at  least  for  the  present.  Although  we 
are  now  dealing  with  the  fundamental  harmonies  of  all  music,  in- 
strumental as  well  as  vocal,  the  student  will  do  well  to  be  governed. 


20 


PARKHURST  HARMONY. 


in  his  choice  of  progressions,  by  the  thought  of  their  being  intended 
for  the  voice,  inasmuch  as  the  easiest  vocal  progressions  are  identical 
with  the  rnost  natural  and  simple  progressions  in  music  universally. 
The  easiest  intervals  for  the  voice  are  the  second  (major  and  minor) 
the  third  (major  and  minor)  the  perfect  fourth,  the  perfect  fifth,  the 
sixth  (major  and  minor)  and  the  octave. 


JDL 


<^ 


XE 


XE 


^-4^^o^i^*%  IQ 


o- 


lac 


■€>- 


Any  interval  larger  than  a  perfect  fifth  will  rarely  be  used  in  the 
present  work.  The  augmented  intervals  (i.e.  augmented  second,  aug- 
mented fourth  and  augmented  fifth),  are  to  be  invariably  avoided. 


I 


tF$^ 


TSL 


t 


rc 


S 


In  general,  it  is  the  smaller  and  the  natural  intervals  of  the  scale  that 
are  to  be  used. 


Three  Primary  Rules  of  Chord-coxxection. 

1st.     Lf^there  he  any  tone  in  common  in  successive  chords,  re- 
tain it  in  the  same  voice.  ~~ 


I 


good. 


bad. 


bad. 


TSl 


^ 


/    if 


« 


jCE 


XH 


«: 


XE 


W 


3Ci: 


xn 


^ 


XE 


g 


xe: 


The  violation  of  this  rule  leads  to  unnecessary  motion  of  the  voices, 
and  a  less  smooth  and  flowing  progression,  as  will  be  seen  above. 

2nd,     Let  the  moving  voices  proceed  to.  the  nearest  tones  in  ihe 
next  harmony.  ~^ 

good.  bad. 


good. 


bad. 


^S 


m 


XE 


xr 


«=^^ 


XE 


^ 


± 


BE 


xx: 


xs: 


XE 


3rd.  //  there  he  no  tone  in  common  in  the  two  chords,  let  the 
three  upper  voices  move  to  the  nearest  tones  in  contrary  motion  to 
the  hass. 


CHAPTER  I. 


21 


9J 


good. 


good. 


bad. 


bad. 


m 


^ 


a: 


o- 


^ 


TW 


m 


5 


XE 


Not  only  is  contrary  motion  in  itself  better  than  parallel, 
but  it  prevents  faulty  relations  between  individual  voices,  which  will 
be  noticed  later. 

In  the  above  illustrations  some  are  marked  "good,"  others,  ''bad.*' 
In  these  and  a!!  future  iUustrations  of  this  sort,  the  pupil  should  play 
the  examples,  and  explain  why  they  are  so  designated.  As  a  rule 
pupils  pay  very  little  attention  to  the  illustrations.  The  teacher  will 
do  well  to  enforce  this  requirement. 

The  Primary  Common   Chords. 

The  following  exercises  consist  of  the  various  combinations  of 
the  Primary  Common  Chords  in  different  scales,  according  to  the 
three  rules  above  given.  Each  exercise  is  to  be  written  three  times, 
first  with  the  octave  of  the  bass,  then  with  the  third,  and  lastly  with 
the  fifth  of  the  chord  in  soprano  in  the  first  chord,  the  other  voices 
taking  the  tones  of  the  chord  lying  nearest  the  soprano.  Care  should 
be  taken  that  the  voices  do  not  lie  too  high  on  the  soprano  clef  (a 
common  fault  with  beginners),  and  never  let  the  soprano  be  higher 
than  G  above  the  staff. 


When  the  bass  is  low,  let  the  other  parts  be  somewhat  lower  also; 
thus  the  following,  though  correctly  harmonized,  has  an  unmusical 
effect,  owing  to  the  great  distance  between  upper  parts  and  bass. 

bad.  good. 

a 


i 


w 


m 


-£i_ 


« 


^ 


jCE 


^ 


For  the  success  of  the  pupil  in  the  following  and  all  future  exer- 
cises, it  must  be  reiterated  that  it  is  not  sufficient  that  the  chord  be 
correctly  written  on  the  staff,  but  the  sense  of  the  effect  must  accom- 
pany the  zcriting.     If  it  cannot  be  done  otherwise,  play  the  exercise 


22 


PARKHURST  HARMONY. 


through,  and  then  read  it  and  recall  the  effect.  By  perseverance  in 
this  matter,  the  abihty  of  the  student  will  increase  as  rapidly  as  the 
combinations  become  more  difficult.  To  write  an  exercise  without 
the  sense  of  the  effect  is  simply  senseless. 

(Each  set  of  exercises  will  be  prefaced  by  an  illustration,  show- 
ing the  use  of  the  chords  involved.) 

Illustration. 


I 


g 


3CX: 


H 


^ 


H 


JOL 


«: 


W 


XT 


« 


Jan 


XE 


P 


xr 


m  ~rr 


no  zsT 


All  the  exercises  should  be  written  according  to  the  laws  of  nota- 
tion, neatly,  and  distinctly. 


Exercises. 
2. 


XH 


3x: 


xn 


P 


-o- 


XE 


XH 


XE 


xn 


3. 

4. 

-r\. 

t» 

1 

•/• 

-^        41 

«> 

- 

«» 

*> 

4-> 

O 

!_<.,> — 1 

•"t^:      I  o  I  *M  ~i — r~~irt~^^i  r^  I 


^ 


O 


xy- 


<♦- 


^ 


XE 


XE 


XE 


XE 


XE 


-*> 


XE 


<^ 


9 

10. 

-»): ,    o 

-o- 

t 

o 

—f    L 

<> 

U 

CY 

^^ 

«> " 

^-^ 

^-^ 

1 

«3 

<3 

o 

11. 


12. 


i 


o -«* 


^ 


XE 


■O 


XE 


-O^ 


IE 


^V 


XE 


XE 


XT"^ XT 


O" 


XE 


O- 


CE 


XT 


The  above  exercises  are  monotonous  because  they  involve  only 
three  distinct  chords.  But  facility  in  these  primary  progressions 
makes  all  others  easier. 


CHAPTER  II. 


23 


Summary. 

Distinction  of  independent  and  dependent  chords ; — Formation  of 
the  Common  Triad  ; — The  root  of  the  triad ; — Reason  for  similarity 
of  effect  in  all  common  triads : — Two  causes  of  variety  in  effect  of 
triads; — Major  and  minor,  perfect  and  diminished  triads: — Tonic, 
dominant  and  suh-dominant : — Why  triads  on  these  three  tones  are 
strongest  and  most  important: — Primary  and  Secondary  triads: — 
Fundamental  harmonies  four-toned: — The  best  tone  of  triad  to  be 
doubled  : — Position  of  a  chord : — Names  applied  to  the  several  tones 
of  a  chord: — Parallel,  contrary  and  oblique  motion: — Which  prefer- 
able:— Which  voices  most  conspicuous: — Best  interval-pro p'essions 
of  each  voice  or  part : — The  forbidden  interval-progressions  : — Three 
Primary  Rules  for  chord-connection. 


CHAPTER  II. 
The  Secondary  Common  Chords. 

The  Secondary  triads  of  the  C-scale  are  these : 


VI  VII 


The  four-toned  harmonies  obtained  from  these  triads  (by  doubhng 
the  root-tone)  are  to  be  used  in  the  same  manner  as  the  Primary 
Common  Chord.  Although  these  Secondaries  are  not  as  important  as 
the  Primaries  they  are  all  effective  (except  the  one  on  the  7th  of  the 
scale,  with  a  diminished  fifth;  this  will  be  spoken  of  later).  In  the 
use  of  these  Secondaries  we  are  governed  mainly  by  the  Primary 
Rules  of  connection  before  given  (on  page  20).  By  following  those 
rules  the  aggregate  effect  of  the  four  tones  of  each  chord  will  be 
good,  although  the  effect  of  any  two  out  of  the  four,  considered  by 
themselves,  will  often  be  more  or  less  inharmonious.  Any  such 
displeasing  effect  is  usually  compensated  for  by  the  harmony  of  the 
full  chord ;  accordingly  the  movement  of  any  two  of  the  voices  in 
their  relation  to  each  other  need  not  ordinarily  be  regarded;  but 
there  are  two  exceptions,  viz : 

No  two  voices  can  ever  move  in  parallel  perfect  fifths  and  octaves. 

Parallel  perfect  fifths  occur  when  any  two  voices,  at  an  interval 
of.  a  perfect  fifth,  moving  in  the  same  direction,  maintain  the  same 
interval  of  a  perfect  fifth  from  each  other,  thus : 


I 


z:6 


-^■^ 


^^=& 


t.# 


24 


PARKHURST  HARMONY. 


They  appear  in  the  following  fonr-part  harmonies, 
bad.  good.  bad.  good.  bad.  good. 


^ 


»=^ 


^m 


^ 


p 


Parallel  octaves  similarly  occur  when  any  two  voices,  at  an  inter- 
val of  an  octave,  and  moving  in  the  same  direction,  maintain  that 
same  interval  from  each  other,  thus: 


They  appear  in  the  following  harmonies : 

bad.  good.         bad.  good. 


i 


=^ 


m 


-d-   -sh 


i 


:S| 


-a-  ^ 


P 


It  will  be  seen  from  the  above  example  that  contrary  motion  is 
an  invariable  preventive  of  these  forbidden  progressions.  While  they 
are  not  likely  to  occur  in  the  use  of  our  present  chords,  when  the 
three  Primary  Rules  are  followed,  there  will  be  danger  of  their  oc- 
currence when  the  harmonies  are  more  complicated.  The  effect  of 
parallel  perfect  fifths  or  octaves  is  always  more  or  less  bad,  and  the 
foregoing  prohibition  is  the  one  invariable  rule  in  fundamental 
harmony. 

A  word  as  to  the  reason  for  the  prohibition. 

Parallel  octaves  are  not  allowed  because,  to  obtain  the  largest 
effect  in  the  succession  of  fundamental  harmonies,  we  must  have  the 
greatest  possible  distinctiveness  of  the  parts.  This  distinctiveness 
is  attainable  in  three  ways ;  viz.,  by  distinctiveness  of  tone,  of  direc- 
tion, and  of  rhythm  (See  Appendix  (C)  ).  The  octave  of  any  tone 
may  be  called  its  higher  self.  Therefore  if  two  parts  move  in 
octaves,  the  individuality  of  one  of  them,  as  regards  both  tone,  direc- 
tion and  rhythm,  is  lost  in  that  of  the  other,  and  the  chords  become, 
for  the  time  being,  essentially  three-part  harmony.     For  the  same 


CHAPTER  II. 


25 


reason  is  it  even  less  allowable  for  any  two  parts  to  be  in  unison  in 
two  successive  chords ;  thus, 


$ 


3CE 


^ 


-^ 


^►^ 


=Sz: 


oo 


^^ 


xr 


XE 


Circumstances  will  sometimes  justify  a  unison  of  two  parts  in  a 
single  chord,  thus : 


w 


f¥^ 


% 


zx 


FS^g^S 


ZX 


oo 


-o- 


3X 


t 


zc 


(This  will  be  spoken  of  again  later.) 

The  prohibition  of  parallel  fifths  is  much  harder  to  explain. 
Their  uniformly  bad  effect  has  always  been  felt  by  writers  upon 
Harmony,  yet  no  one  has  succeeded  in  giving  a  simple  and 
lucid  explanation  of  the  matter.  The  best  that  can  be  offered 
will  certainly  be  somewhat  abstruse,  and  not  being  practically  nec- 
essary the  pupil  will  find  it  stated  in  the  Appendix  (D).  It  will 
suffice  to  say  here  that  they  are  forbidden  from  the  simple  fact  of 
their  unpleasant  effect,  which  is  never  entirely  concealed  by  the  ad- 
dition of  the  remaining  tones  of  the  chords.  The  universality  of 
the  prohibition  of  either  parallel  fifths  or  parallel  octaves  is  not  be- 
cause their  effect  is  so  much  worse  than  that  of  many  other  pro- 
gressions ;  but  because  in  every  instance,  a  certain  degree  of  pos- 
itively bad  effect  is  evident.  The  movement  of  two  voices,  at  other 
intervals  from  each  other,  is  often  much  more  objectionable  than 
parallel  fifths  or  octaves. 

But  in  respect  of  all  other  movements,  circumstances  so  far  alter 
cases,  that  a  movement  that  is  bad  in  one  circumstance  is  good  in 
another ;  whereas  parallel  fifths  and  octaves  are  never  so  modified  by 
circumstances  as  to  produce  a  good  effect. 

Let  the  following  exercises,  involving  the  primary  and  second- 
ary common  chords,  be  written  with  a  strict  observance  of  the  Three 
Primary  Rules. 


26 


PARKHURST  HARMONY. 
Illustration. 


I 


x: 


P    \fiCl    I  '^-fi 


^ 


S 


^ 


^^ 


33r 


^sf—a. 


A  better  flow  of  harmony  is  often  obtained  by  placing  the  third 
or  £fth  of  the  first  chord  in  the  soprano,  instead  of  the  octave  of  the 
root.  If  the  soprano  is  to  be  the  third  or  £fth,  it  is  indicated  by  a  3 
or  '5  placed  under  the  first  bass  note.  Otherwise  let  the  soprano 
be  in  octave  with  the  bass.  This  rule  must  ahvays  be  carefully 
observed.  Use  judgment  also  as  to  which  third  or  fifth  shall  be 
chosen.  The  following  shows  the  difference  between  a  poor  and  a 
good  choice. 

^^^'    -  good. 


I 


ft 


^ 


5^ 


^ 


?^ 


tL 


XT 


XE 


XE 


Exercises. 


1. 


'^ 


^ 


— ^r-a 


r  ir  -^  If  ^^  If  j^ 


xn 


.ix= ^-=^-p — e--J—:^'^-s .-u-^^s^a. 1 

^.     rj    y....\.  .   A".           \ |J — 1 — 1  [     ti    II      — \^ — 1 — 1  IT  |[ 

3^^ 


«55^ 


^ 


~^^ 


^ 


TJl 


S 


P 


^ 


^ 


yif--  irnf 


^^ 


g)   '  <>      .'  o 


s 


^^Ff-tr^N"i^^^^-^-f 


CHAPTER  II. 


27 


^ 


^ 


'^  f  I  '^  J 


^ 


'fW 


3 


^ 


^ 


10 


^ 


=551: 


^ 


^^IJ^^T  ^ 


The  Closing  Chord  of  Every  Composition. 

Exery  a)mposition  closes  with  the  Tonic  chord,  because  this 
alone,  of  all  the  seven  chords  of  the  scale,  has  the  nature  of  complete 
rest.  This  terminal  effect  of  the  Tonic  chord  varies  somewhat  ac- 
cording to  the  element  of  the  chord  that  is  in  the  soprano  (octave, 
third,  or  fifth  from  the  root),  being  weakest  when  the  fifth  is  in 
soprano : 


I 


^-^ 


^ 


4^:     a    (^ 


§ 


^ 


JOL 


stronger  with  the  third  in  soprano: 


^ 


i 


^ 


i^Yp  r^ 


§ 


^ 

TT 


jDE 


^nd  strongest  wjth_soprano  on  the  Tonic 

m 


w 


3 


«= 


XE 


(The  pupil  should  carefully  compare  the  three  effects  of  the  Tonx 
chord  in  these  three  positions,  and  also  examine  the  closing  chord  o^ 
various  vocal  and  instrumental  compositions,  where  he  will  find  that 
the  vast  majority  close  with  the  Tonic  in  the  highest  part,  that  with 
comparative  in  frequency  the  third,  and  very  rarely  the  iifth,  occurs 
in  the  highest  part. 


28 


PARKHURST  HARMONY. 


This  matter  of  the  close  is  discussed  more  fully  in  a  later  chapter 
under  the  subject  of  Cadence). 

It  is  better  sometimes  to  violate  the  Primary  Rule  of  retaining 
in  the  same  voice  the  tone  common  to  two  chords,  when  thereby  the 
final  chord  of  an  exercise  can  be  brought  into  a  more  effective  posi- 
tion for  the  close,  thus : 


fMn 

p— 

-«- 

bette 

-js — 

r. 

p*= r 

rq 

F 

bettei 

-^ 

wM 

S— 

-*^ 

1— 

-^ 

w 

^^ 

U 

— 

rr-  f 

=^ 

-|S> — 

t^ 

1 

f=\^ 

"~¥TI 

f  ...  1 

L 



1 

In  any  other  part  of  the  exercise,  the  Primary  Rule  should  be 
followed,  in  such  cases  as  the  above,  so  as  to  avoid  the  effect  of  a 
close. 

When  a  bass  note  is  repeated  in  the  same  measure  an  octave 
above  or  below,  the  harmony  can  either  be  written  in  whole  notes,  or, 
which  is  often  better,  a  different  position  can  be  chosen.  In  the  latter 
case  it  is  usually  preferable  that  the  upper  voices  should  move  in 
contrary  motion  to  the  bass,  although  parallel  motion  is  allowed. 


I 


Tf 


^ 


XE 


^ 


O""^ 


cr 


i 


JZ^ 


f 


SEESEf 


p    fi^~. 

—T% 

___ 

rq 

♦4! b^ 

=8= 

^ 

-a 

— 1 — f — 

=^ 

^ 

^ 

"^ 

^ 

ry 

• 

XT 

^^=^ 

11 

ZZJ 

-  s) 

,4» 

r^ 

hJ 

d- 

=d 

*•    : 

In  the  following  brief  exercises,  which  we  will  regard  as  clos- 
ing fragments,  bring  the  soprano  upon  the  keynote  in  the  final  chord. 


Wf^ 


3, 


(P  rp 


^==?z 


ax 


xi: 


e 


m 


3CE 


^ 


^ 


? 


XE 


CHAPTER  IL 


29 


In  the  following,  bring  the  soprano  upon  the  third  in  the  final 
chord. 


1. 


'6. 


4. 


^ 


s 


^TP 


<s^-P 


Ol 


^ 


XE 


IE 


^22 


The   Leading  Tone. 

A  close  examination  of  the  tones  of  the  diatonic  scale  discloses 
the  fact  that  they  differ  from  each  other  in  their  natural  tendency  as 
regards  movement.  Some  of  them  are,  as  it  were,  equally  poised, 
and  the  remainder  have  a  more  or  less  pronounced  tendency  dozvn- 
ivard  or  upzvard.  In  the  Appendix  (E)  the  scale  is  more  completely 
analysed  in  this  respect.  For  the  present  we  have  to  do  with  the 
tendency  of  only  one  tone  in  the  scale,  the  seventh.  By  carefully 
noticing  the  quality  of  this  tone,  it  will  be  found  to  lead  very  evi- 
dently up  to  the  eighth,  the  Tonic,  and  is  generally  denominated  "the 
leading  tone."  It  is  a  mistake  to  suppose  this  to  be  the  only  tone  that 
has  the  leading  quality ;  but  it  is  so  pre-eminent  in  this  above  all  the 
others  that  it  is  rightly  called  "the  leading  tone".  The  stiffness  and 
unnaturalness  of  many  a  pupil's  exercises  is  in  a  measure  due  to  a 
disregard  of  this  natural  leading  of  the  seventh;  and  this  gives  oc- 
casion for  insisting  again  upon  the  necessity  of  knowing  the  effect  of 
each  chord,  which  is  so  often  the  only  guide  in  choosing  a  good 
progression. 

When  a  chord,  containing  the  leading  tone  in  the  soprano,  is 
followed  by  one  containing  the  Tonic,  it  is  generally  better  for  the 
^i^rano  to  move  to  the  Tonic,  thus : 

b. 


Example  (b)  is  in  strict  accordance  with  the  third  Primary  Rule, 
tut  the  progression  at  (a)  is  better,  because  more  natural.  This 
exception  to  the  rule  occurs  when  the  common  chord  on  the  Domi- 
nant (with  the  leading  tone  in  soprano)  is  followed  by  the  common 
•chord  on  the  sixth  of  the  scale,  as  in  the  example  above. 

Let  the  pupil  harmonize  the  following  fragments  according  to  the 
foregoing  exception. 


30 


PARKHURST  HARMONY. 


2. 


^ 


*!? 


P 


m 


22 


2Z 


3EX: 


^ 


5F 


§ 


^ 


o- 


*: 


When  the  leading  tone  occurs  in  an  inner  voice,  in  the  above  suc- 
cession of  chords,  it  is  not  necessary  to  follow  its  natural  progres- 
sion, not  because  the  inner  voice  does  not  feel  the  impulse  upward  as 
strongly  as  the  soprano,  but  because,  being  an  inner  voice,  it  is  less 
conspicuous  to  the  hearer,  and  the  downward  motion  will  secure 
fuller  harmony,  thus: 

b.   I  c. 


m 


E35 


=  =zs 


m 


good.      less  good.      bad 


At  (b)  we  have  only  three-part  harmony,  at  (c)  four-part  har- 
mony, but  parallel  fifths  between  soprano  and  bass. 

The  object  of  the  following  exercise  is,  to  impress  the  leading 
tone  upon  the  pupil's  mind.  Wherever  the  dominant  chord  (with 
"leading  tone"  in  soprano)  is  followed  by  the  chord  on  the  sixth  of 
the  scale,  let  the  progression  from  leading  tone  be  upward ;  the  other 
voices  downward  as  usual ;  but  in  the  same  succession  of  chords,  with 
leading  tone  in  a  middle  voice,  let  the  progression  be  downward. 

In  that  position  of  the  chord  wherein  the  leading  tone  occurs  jn 
the  tenor,  it  is  sometimes  more  judicious  to  lead  up  into  unison  with 
the  alto,  even  at  the  expense  of  losing  one  tone  of  the  harmony.  For 
although  the  tenor  is  an  '.'inner  voice",  its  progression  is  in  general 
more  conspicuous  than  that  of  the  alto.  Accordingly  the  progression 
at  (a)  is  somewhat  preferable  to  that  at  (b). 

a.  b. 


I 


^m 


Ct 


Illustration. 


S3 


^-16 


^ 


=s 


-s- 


i 


^ 


m 


i 


^^=F 


XX 


CHAPTER  II. 

Exercises. 


31 


■*)• "  1    f  ^-f^'-^-^-f^- — p — 1    III    1  1 — n 

'\r  ^nr- 


xn 


««— ^ 


3. 


S 


rirnrr|ff|M 


XE 


f^mn 


ky  ;   fi> 


rt^tf^i^ 


The  movement  of  the  soprano  in  the  following  example,  from  the 
leading  tone  to  G  (di) ,  is  still  more  unnatural  and  offensive  than  its 
movement  to  A  (b). 


i»j    a.        b 

■ffr)    o-<-" 

«^ 

*):     1    -■ 

^3 

U fil u 

-^ 

M 

The  foregoing  progression  at  (a)  which  is  utterly  inadmissible  in 
the  soprano,  is  to  be  allowed  in  an  inner  voice,  because  less  apparent, 
and  is  very  often  desirable,  as  affording  a  fuller  harmony. 


ri~li 

bry-- 

I 
-If 

). 

TlT» 

pin 

tf 

>):  1 

^ 

1^ 





^ 

"^4^ 

rz^ 

Lj-J 

it 

uu 

t> 

1-9— J 

t » 

This  progression  (a)  is  especially  desirable  at  the  close  of  an 
exercise,  in  order  to  have  the  final  chord  in  full  harmony,  with 
soprano  on  the  Tonic. 

The  above  descent  from  the  leading  tone,  when  in  the  middle 
voice,  is  to  be  avoided  when  the  bass  also  descends,  for  in  this  case 
all  the  voices  descend,  thus: 


32 


PARKHURSr  HARROW. 


g'ood. 


bad. 


bad.. 


better 


JJL 


-o- 


s 


i 


^ 


-oo 


i± 


From  the  foregoing  we  deduce  the  following  rule;  in  the  pro- 
gression from  the  dominant  to  the  tonic  chord,  the  leading  tone  can 
descend  a  third,  when  in  an  inner  voice,  if  the  bass  ascends:  other- 
wise it  must  ascend.* 

The  following  closing  fragments  are  designed  to  accustom  the 
pupil  to  this  manner  of  treating  the  leading  tone. 

Illustration. 


% 


^ 


i 


m 


:z^m 


2Z^ 


-*>- 


XE 


Exercises. 


j/nrri^rrirJr[ft'i»ii>fMLif 

4-  5.^  ,  6.  7. 


XE 


..■iiiij'lljjl  ili'JiirMi'iirirrirr|.|| 


The  Diminished  Triad, 


W 


The  triad  on  the  seventh  of  the  scale  is  different  from  all  the 
others  in  having  a  diminished  fifth.  In  doubling  the  root-tone  for 
four-part  harmony  the  soprano  can  take  either  the  octave,  third  or 
£fth. 


♦Althoujrh  this  is  the  usual  rule  prescribed  in  text  books,  the  erreat  harmonUt  Sebastian 
Bach,  is  authority,  in  some  of  his  chorals,  for  leading  all  the  voicrs  i\o\\  n. 


CHAPTER  II. 


33 


fe^S=tid 


f^; 


w 

bail. 


XE 


bad. 

_Ol_ 


bad. 


By  doubling  the  root-tone  we  have  tzco  Icadiji^^  tones,  so  that 
neither  of  the  above  chords  is  satisfactory.  The  best  of  the  three  is 
the  one  with  soprano  in  the  third,  for  this  somewhat  conceals  the 
octave  of  the  bass,  which  is  in  the  alto.  By  doubling  the  third  or  the 
fifth  we  better  ourselves  somewhat. 


i 


«= 


m 


JQL 


:§: 


3x: 


AX 


But  almost  any  connection  of  either  of  these  forms  with  the  other 
common  chords  is  awkward  and  displeasing.  In  whatever  connec- 
tion and  in  whatever  form  this  chord  appears,  it  bears  the  stamp 
of  the  diminished  fifth,  which  usually  prevents  its  adoption  in  simple 
harmonic  progressions.  The  occasional  opportunity  for  its  use  will 
be  shown  later. 


The  Incidental  Alteration  of  the  Common  Chord. 

Hitherto  we  have  used  only  the  natural  tones  of  the  scale  in 
forming  the  chords.  While  the  integrity  of  the  scale  and  the  clear- 
ness of  the  harmony  require  that  in  the  main  the  chords  should  be 
thus  composed,  monotony  would  inevitably  ensue  if  this  rule  were 
invariable.  The  occasional  substitution  of  an  accidental  tone  for  a 
normal  tone  does  violence  neither  to  the  scale  nor  to  the  harmony, 
and  casts  an  agreeably  new  complexion  upon  the  flow  of  harmonies. 
Compare  the  following : 


22: 


m 


i 


zt« 


xi: 


« 


XI 


2=5 


22: 


^ 


W- 


M 


m 


» 


m 


and  the  third  chord  will  be  found  more  pleasing  with  the  F#  than 
with  the  normal  tone  on  that  degree  of  the  scale.  The  pupil  is  not 
to  confound  this  with  modulation ;  such  a  use  of  accidentals  is  not 
modulation,  as  will  be  explained  later. 


34 


PARKHURST  HARMONY, 


The  subject  of  Modulation  is  fully  discussed  in  Chapters  XVIII- 
XIX. 

Accidentals  thus  used  commonly  affect  the  third  in  the  chord, 
very  rarely  the  fifth,  and  when  one  is  placed  under  a  bass-note  it  is  to 
be  understood  as  belonging  to  the  third  from  the  bass,  thus : 


I 


m 


i 


^ 


& 


xr 


XE 


1^ 


3x: 


n^^ 


XT 


^ 


^        X        i  T 

The  use  of  accidentals  to  affect  the  third  is  commonly  to  change 
a  minor  third  to  a  major. 

The  following  exercises  give  practice  in  the  use  of  accidentals. 
The  above  example  will  suffice  as  an  illustration. 

Exercises. 


i 


f 


^ 


XE 


z. 


Tx: 


^ 


2Z 


4, 


XT 


s 


T— 1 


^ 


22 


5        ^ 

Summary. 
Secondary  triads : — Parallel  perfect  fifths  and  octaves : — The  way 
to  avoid  them : — Reason  for  bad  effect  of  parallel  octaves : — Distinc- 
tiveness of  parts  is  three-fold: — Successive  unisons: — Reason  for 
the  invariable  prohibition  of  only  parallel  perfect  fifths  and  octaves, 
if  they  do  not  produce  the  worst  effect  of  all  progressions: — Rela- 
tive value  of  octave,  third  and  fifth  in  soprano  in  last  chord: — Re- 
laxing Primary  Rule,  to  bring  soprano  on  the  Tonic  in  last  chord : — 
Procedure  when  bass  moves  an  octave : — Leading  tone : — Exception 
to  third  Primary  Rule : — Movement  from  '^leading  tone"  when  in  an 
^'inner"  voice : — proper  progression  from  "leading  tone"  in  different 
voices,  when  dominant  chord  is  followed  by  that  of  the  Tonic — 
Diminished  triad,  and  doubling  its  root  in  four  part  harmony : — Use 
of  accidentals : — Which  element  of  chord  usually  affected  by  them : — 
Accidentals  used  to  change  a  minor  third  to  a  major. 


CHAPTER  III. 


35 


CHAPTER  III. 
The  Minor  Scale  and  its  Triads. 

The  scale  heretofore  used  has  been  the  Diatonic  Major  Scale.  As 
already  remarked,  the  several  tones  of  this  scale  constitute  a  sort  of 
organism,  by  reason  of  the  internal  relation  of  the  tones  to  each 
other.  But  there  is  still  another  series  of  tones  which  shows  itself 
to  be  equally  an  organism,  with  corresponding  relation  of  the  several 
tones  among  themselves,  and  equally  melodic,  yet  with  a  surprisingly 
different  effect,  from  the  simple  fact  that  the  intervals  of  tones  and 
semitones  succeed  each  other  in  different  order. 

The  Diatonic  Major  scale  of  C 


$ 


XI- 


TF^ 


>o  ^> 


is  a  sample  of  the  scale  thus  far  used  in  our  work.  This  can  be 
transformed  into  another  scale,  equally  coherent,  by  changing  the 
major  third  above  the  Tonic  into  a  minor  third,  and  the  7najor  sixth 
into  a  minor  sixth,  thus: 


I 


:cF-^ 


xn 


o: 


XE 


This  is  not  so  melodic  throughout  as  the  preceding  scale,  on  account 
of  the  gap  between  Ab  and  B.  To  avoid  this  interval  of  an  aug- 
mented second,  the  melody,  when  proceeding  by  degrees  upward  from 
G,  takes  A,  which  divides  the  space  between  G  and  B  into  two  equal 
intervals,  thus : 

unmelodic.  melodic. 


I 


XE 


l^O    »      ^i^  1., 


l?o  <* 


IX 


O  ^^  V2     Viz  .^.O  ^''^ 1 T 

In  connection  with  harmony  it  appears  as  follows : 


i 


i 


t 


3X1 


^ 


^ 


i 


xr 


bad. 


^ 


ffl 


good. 


^S 


s 


H 


But  even  as  the  melodic  tone  the  Aif  is  not  invariably  used,  for  if 
the  6th  degree  of  the  scale  is  not  followed  immediately  by  the  7th, 
then  the  6th  deeree  will  be  Ab,  thus. 


36 


PARKHURST  HARMONY. 


^S 


i 


m 


3 


? 


ps 


^ 


33t 


-^      i2 


xx: 


4u 


^ 


S 


xc 


XE 


3i=:xi 


We  may  then  regard  Ab  as  the  normal  tone  of  this  scale,  and  A^ 
as  the  occasional  substitute,  for  the  sake  of  a  smoother  melody.  But 
as  the  harmonic  tone,  i.e.,  as  the  root  or  any  element  of  the  chord, 
the  6th  degree  must  always  be  Ah,  thus : 


good 


XE 


& 


i 


3Jr 


*« 


m=^ 


i 


& 


bi 


d. 


P 


^^ 


^=?z 


jix: 


3CE 


[#=i 

"fiV 

■k- 

^k); 1 

6 

1 ' 

[■ 

^ 

-4^ 

bn 

— c 

h    '  . 

?^= 

& 

) G 

••■'■  cl 

— o 

**      ] 

This  form  of  the  scale 


I 


bo  t» 


o 


i>»"  " 


is  accordingly  called  the  harmonic  form,  and  the  following, 


TJ 


jlQ^lO^^^ 


^3r 


the  melodic  form.  But  while  the  ear  is  satisfied  with  the  above,  as  an 
upward  melodic  scale,  the  effect,  in  reverse  direction,  is  quite  in- 
congruous : 


I 


a. 


bad. 


good. 


t^^ 


33: 


«»  o  « 


*  bo  ^ 


IX 


"  "  bo-TT 


We  must  therefore  have  an  altered  form  for  the  descending  scale, 
which  is  found  above  at  (b).  The  necessity  of  this  form  is  shown, 
more  clearly  by  combining  each  of  the  above  forms  with  harmony : 


CHAPTER  in. 


37 


I 


u 


i^ 


'bad. 


rf 


*-# 


f 


^ 


i 


goodJ 


r 


m 


A 


g 


22: 


f 


f 


We  thus  have  three  different  forms  in  our  new  scale;  the 
harmonic  (ahke  up  and  down),  the  melodic  upzvard,  and  the  melodic 
downward. 

harmonic. 


tf       ZTE 


m 


XF 


bo  i» 


OE 


17TT- 


XE^ 


XT 


up- 


melodic. 


down. 


^^=^ 


^n 


xfzzzn 


iX 


o  1^ 


-o- 


:is^ 


o 


3X 


XT 


This  new  scale,  in  its  collective  forms,  is  called 


The  Diatonic  Minor  Scale. 

It  is  so  called  because  we  obtained  it  by  changing  the  major  third 
and  major  sixth  of  our  previous  scale  into  minor  third  and  minor 
sixth.  ( Similarly  the  previous  scale  takes  its  name  of  major  from  its 
^rmjor  third  and  major  sixth.) 

On  comparing  the  major  and  minor  diatonic  scales,  we  are  at 
once  impressed  with  the  distinctive  character  of  each.  In  the 
German  language,  which  is  so  apt  in  the  significance  of  its  terms, 
the  major  is  called  hard  (Dur),  the  minor,  soft  (Moll).  The  major 
is  vigorous  and  manly ;  the  minor  feminine  and  tender ;  the  one, 
strong;  the  other,  weak.  Moreover  the  minor  scale  is  proverbially 
sad,  and  cannot  be  joyous.  While  Milton's  L' Allegro  is  emphatically 
major,  II  Penseroso  is  equally  minor  ;  and  yet  Handel's  "Dead  March 
in  Saul"  is  striking  evidence  of  the  capacity  of  the  major  scale  to 
express  the  deepest  sadness,  for  this  composition  is  thoroughly 
major,  containing  not  even  a  single  minor  chord.  The  tonic  and 
dominant  chords  comprise  the  bulk  of  its  contents.  The  major  scale 
is  thus  more  versatile  than  the  minor  in  the  diversity  of  its  power. 
But  there  is  a  sort  of  self-possession,  a  dimly  defined  hope,  in  the 
sorrow  of  a  major  composition.  The  mood  of  the  minor  scale  is 
the  sadness  of  despair. 

Again,  looking  at  these  two  scales  from  another  point  of  view,  we 
see  that  the  major  is  characterized  by  simplicity ;  it  is  invariable,  up 
and  down.  The  minor  is  complicated,  having  three  forms.  This  in- 
creases the  difficulty  in  its  correct  use,  but  at  the  same  time  stamps 


38  PARKHURST  HARMONY. 

this  scale  as  being  richer  in  its  contents  than  the  major,  as  there  are 
two  more  tones  involved  in  it. 

If  instead  of  beginning  the  minor  scale  upon  C  we  begin  it  upon 
A,  and  have  the  successive  intervals  exactly  correspondant  v^^ith  those 
in  the  minor  scale  of  C,  in  the  several  forms,  v^e  obtain  the  following 
harmonic  and  melodic  scales  of  A  minor. 

harmonic. 


4%   o  ^' 


331 


i»    O 


XE 


-»/5 


^ -^2 te- 

up.  melodic.  down 


31: 


^ 


-^ 


m 


3X 


3aL 


-% te- 

In  the  harmonic  scale  tlie  semitones  occur  between  the  2d  and 
3rd,  the  5th  and  6th,  and  the  7th  and  8th.  In  the  melodic,  up,  be- 
tween the  2d  and  3rd,  and  7th  and  8th.  In  the  melodic,  down,  be- 
tween the  2d  and  3rd,  and  5th  and  6th. 

As  to  the  reason  for  having  two  forms  of  the  melodic  scale,  see 
Appendix  (F). 

It  will  be  seen  that  the  scales  of  C  major  and  of  A  minor 
are  closely  linked  together ;  for  in  beginning  the  minor  scale  upon  A 
we  find  our  minor  third  and  minor  sixth  already  prepared  to  hand. 
The  harmonic  form  therefore  requires  only  the  substitution  of  G# 
for  G ;  the  upward  melodic,  the  use  of  F#  and  G#,  while  the  dozvn- 
ward  melodic  scale  comprises  the  identical  tones  of  the  major  scale 
throughout.  This  degree  of  identity  of  the  tones,  and  the  consequent 
identity  of  form  of  the  triads  on  A,  B,  D,  and  F, 


<l  ^  4i  U  » 


which  make  the  passage  from  the  one  scale  to  the  other  very  easy, 
cause  them  to  be  called  relative  scales ;  that  is,  the  relative  minor 
of  C  major  is  A  minor,  and  the  relative  major  of  A  minor  is  C  major. 
Similarly,  the  relative  minor  of  any  major  scale  begins  a  minor  third 
below,  and  conversely,  the  relative  major  of  any  minor  scale  begins  a 
minor  third  above.  Furthermore  the  great  degree  of  identity  of 
tones  of  a  minor  scale  with  those  of  its  relative  major  causes  that 
the  signature  of  a  minor  scale  is  the  same  as  that  of  its  relative 
major. 

The  necessity  of  a  semitone  between  the  7th  and  8th  of  the  scale 
is   the  requirement  of  the  leading-tone-quality  in  the  7th,  which  is 


CHAPTER  III. 


39 


as  essential  to  the  minor  as  to  the  major  scale.    Compare  the  follow- 
ing: 

X  X 


$ 


3X 


t 


XH 


XX 


xi-^ 


T¥  -«- 


x> 


If  the  7th  were  to  be  invariably  raised,  the  accidental  could  be  put 
into  the  signature ;  but  as  we  have  seen,  the  accidental  is  omitted  in 
the  downward  melodic  scale,  so  that  the  simplest  way  is  that  it  be 
always  expressed  when  needed. 

The  first  great  difficulty  in  the  study  of  Harmony  is  in  the  use  of 
the  minor  scale.  For  this  reason  a  full  and  explicit  statement  of  its 
construction  has  been  given.  To  insure  a  reasonable  degree  of 
familarity  with  its  complexities,  it  is  now  required  of  the  pupil  that, 
according  to  the  model  furnished  above  in  the  scale  of  A  minor,  he 
should  write  all  the  following  minor  scales  in  the  harmonic  and 
melodic  forms,  in  the  several  signatures. 


^>^^i<*it  o  ii^ri^A  0  \\h\ ,  mf 


-t>- 


vv-gt.^^  ^  h\\  o  \w^^   I 


55? 


-€>^ 


I 


Write  the  same  in  the  bass  clef : 


ll"     ll*.!"!!      ||Hi»»|,       llJAj* 


ty 


XT 


u 


s 


^ 


& 


^^:^ 


xr 


XE 


-^ 


The  purpose  of  the  above  exercise  will  be  fully  attained  only 
when  the  effect  of  each  form  becomes  Hxed  in  the  mind.  The  pupil 
can  well  afford  to  spend  the  time  necessary  for  the  complete  mastery 
of  this  scale ;  for  without  it,  he  will  be  constantly  liable  to  embarrass- 
ment and  consequent  inaccuracy  in  its  use. 

The  Triads  of  the  Minor  Scale. 
The  triads  of  the  scale  of  A  minor  are  as  follows : 


I 


|.#X  U<^§  M: 


40 


PARKHURST  HARMONY. 


Those  on  the  £rstj  fifth  and  fourth  of  the  scale  are  the  Tonic,  Domi- 
nant, and  Subdominant  triads,  as  in  the  major  scale.  But  only  one  of 
them,  the  Dominant,  is  a  major  triad.  In  addition  to  major,  minor 
and  diminished  triads,  we  here  meet  with  a  new  form,  founded  on 
the  third  of  the  scale  (C),  containing  an  augmented  fifth  by  reason 
of  the  raised  7th  (G#).  This  triad  is  called  the  augmented  triad. 
As  the  7th  of  the  scale  is  not  invariably  raised,  the  accidental  must 
be  indicated  when  wanted.  In  the  augmented  triad  it  is  indicated  by 
prefixing  it  to  the  figure  5,  placed  under  the  bass  note,  as  that  is  the 
interval  from  the  bass. 


I 


m 


i 


t 


^^F^ 


* 


XE 


& 


XE 


#5 


kl5 


A  line  through  a  figure  is  equivalent  to  a  ^  before  the  figure, 
thus  ^=#5. 

The  dominant  chord  of  the  minor  scale  contains  the  raised  7th 
as  the  third  of  the  chord,  and,  as  already  explained,  the  simple  acci- 
dental, without  a  figure,  is  placed  under  the  bass  note : 


I 


^m 


m 


s 


its: 


xn 


a 


T 


In  writing  the  following  exercises,  place  first  the  octave,  then  the 
third,  and  lastly  the  fifth  in  the  soprano  of  the  first  chord. 


Illustration. 


CHAPTER  III. 


41 


1. 


m 


Exercises. 
2. 


JOE 


XE 


XT 


^ 


-^^ 


3x: 


^ 


^ 


TJL 


& 


3s: 


XE 


3x: 


(>. 


^ 


BOl 


XJl 


3i: 


an 


-o- 


8. 


E 


XE 


S 


g 


-O- 


^ 


XE 


3CE 


XE 


As  the  raised  yth  is  such  a  significant  tone  of  the  minor  scale, 
in  order  to  impress  it  upon  the  mind,  let  the  pupil  write  out,  for  him- 
self, the  dominant  chord  with  the  necessary  accidental  in  each  sig- 
nature up  to 


^ 


* 


and 


tes 


The  Augmented  Second. 
The  chief  difficulty  in  the  use  of  the  minor  scale  arises  from  the 
interval  of  an  augmented  second  between  the  6th  and  7th  of  the  scale, 


A 


imnor 


'    ^^ 


% 


which  is  a  prohibited  interval  in  all  fundamental  progression, 
Q\ving  to  its  difficulty  and  unnaturalness.  The  voices  must  therefore 
be  so  disposed  that  none  will  be  obliged  to  take  this  interval.  The 
difficulty  occurs  chiefly  in  the  connection  of  the  chords  on  the  5th 
and  6th  of  the  scale,  thus: 


42  PARKHURST  HARMONY. 

The  above  faults  are  avoided  by  the  following  progression : 


i 


^ 


m 


XE 


XH 


XH 


m 


TF 


3CE 


■^~r 


This  is  the  only  progression  possible  in  the  combination  of  these 
two  chords.  In  such  combination  neither  the  root  nor  the  Hfth  in  the 
chord  on  the  6th  of  the  scale  can  be  doubled.  The  procedure  in  the 
connection  of  these  two  chords  is  expressed  in  the  following  law : 

We  must  invariahly  double  the  third  in  the  chord  on  the  6th  of 
the  minor  scale,  when  that  chord  is  preceded  or  follozved  by  the 
dominant  chord.  This  doubling  can  be  either  in  unison  or  in  octave, 
thus: 


I 


unison. 


unison. 


octave. 


unison. 


unison. 


octavo. 


XE 


XE 


SE 


m 


^ 


m 


^ 


XE 


m 


TSST 


m^m 


XBX 


XJ 


■^^ 


m 


-o- 


XE 


XE 


XE 


jCE 


XE 


X£ 


T 


The  difficulty  in  the  connection  of  these  two  chords,  and  the  sin- 
gle solution  of  the  difficulty,  must  be  clearly  understood,  as  the  fre- 
quent embarrassment  in  the  writing  of  exercises  in  the  minor  scale 
will  be  found  to  center  in  this  very  point.  The  following  exercises 
will  give  facility  in  the  combination  of  these  chords. 


Illustration. 


m 


m 


i 


SSI 


^1 


M 


33C 


^8^ 


^r 


m 


^ 


m 


XE 


J 


Let  attention  always  be  given  to  the  position  of  the  iirst  chord  of 
each  exercise,  as  indicated  by  the  figuring.  Carelessness  in  this  re- 
spect is  certainly  inexcusable. 


CHAPTER  III. 


43 


Exercises. 
2. 


m 


■J  M  J  I'r.WhJ^ 


fO       r-^         r.      C* 


-O— 


>):l4Mrf  irfi^^ 


q17 


3X1 


^ 


6. 


xx: 


-o- 


7. 


s 


8. 


.3 


^ 


^^ 


3X 


*>:l\^irr' 


10. 


fefe#^ 


XE 


-^ 


f-^ 


^^ 


13. 


^s 


m 


14. 


15. 


3 


3X 


16. 


m 


^ 


-G- 


^ 


a 


XE 


^ 


1 

In  the  connection  of  the  chords  on  the  2nd  and  5th  of  the  minor 
scale,  the  rule  of  retaining  in  the  same  voice  the  tone  in  common 
rnust  be  violated  in  order  to  avoid  the  progression  of  an  augmented 
second,  thus: 


As  seen  above,  the^nly  way  to  avoid  the  fault  is  to  have  all  the 
upper  voices  descend,  even  though  the  bass  descend.  The  following 
fragments  introduce  this  difficulty,  and  also  the  preceding,  in  differ- 
ent scales. 

Illustration. 


m 


^ 


xx: 


-^ 


zz: 


m 


i 


44 


PARKHURST  HARMONY. 

Exercises. 

^2.  s.     ,  4. 


■7^' If  I  iiyiJfi"ii«/ji.i,ii°ii»iWifrii 


g'i"ii^'vjirf;rri 


i 


f 


■c*- 


g>  '^z 


There  are  two  diminished  triads  in  the  minor  scale,  on  the  2nd 
and  on  the  7th  degrees, 


in  A  minor 


W 


F^=^ 

irH- 

— i» 

instead  of  only  one,  as  in  the  major  scale.  The  resources  ot 
the  minor  scale  are  not  to  be  judged  by  the  use  of  the  sim- 
ple chords  thus  far  presented,  for  after  deducting  the  three  chords, 
on  the  2nd,  3rd  and  7th  of  the  scale, 


in  A  minor 


^5 

which  arc  less  effective  because  of  the  diminished  fifth  in 
two  of  therri^  and  the  augmented  fifth  in  the  third,  we  have  only 
four  remaining.  But  it  will  be  none  the  less  advantageous  for  the 
pupil  to  work  out  the  following  exercises,  with  a  strict  observance 
of  all  the  foregoing  rules.  As  a  precaution,  look  through  each  bass, 
before  writing  the  harmony,  to  see  if  the  5th  and  6th  of  the  scale 
are  in  immediate  connection,  so  as  to  double  the  third  in  the  chord 
on  the  6th. 

Illustration. 


^^ 


j4#dE 


* 


m 


It5 


? 


m 


f 


XE 


CHAPTER  IV. 


4S 


Exercises. 


a 


^^;nfL-lNlr- 


m 


2. 


«5? 


e 


^ 


22 


-« H& 


3.  , 


xz: 


-«— «^ 


'     \rJ    ^      I 


^^T 


t.    ||.j|..-^4^ 


^^^H^i — p-'^'-T' — J — —^ \  {'  \P — ht-i If 

y  '^i  ^  rji  [  N  J  ir  J  u  1  1^^  ujioj 

m 


*^ 


22==  =  :^ 


f 


^^^ 


Summary. 

How  the  major  scale  is  transformed  to  the  minor: — ^Why  the 
minor  is  less  melodic  than  the  major: — How  the  minor  scale  is  made 
melodic: — The  three  forms  of  the  minor  scale: — Points  of  con- 
trast in  the  major  and  minor  scales: — Why  the  A  minor  scale  is 
called  the  "relative  minor"  of  C  major : — Interval  between  keynotes 
of  every  major  scale  and  its  relative  minor: — Signature  of  every 
minor  scale : — Why  the  accidental  that  produces  the  "leading  tone" 
in  the  minor  scale  is  not  expressed  in  its  signature : — Classification 
of  triads  in  minor  scale: — How  the  raised  fifth  in  the  augmented 
triad  is  indicated : — How  the  alteration  of  the  third  in  a  chord  is 
indicated : — Chief  difficulty  in  use  of  minor  scale : — Why  augmented 
second  is  prohibited: — In  the  connection  of  what  chords  the  aug- 
mented second  is  most  likely  to  occur : — In  such  connection  what  law 
to  be  followed  : — Rule  in  the  connection  of  chords  on  the  2nd  and  5th 
of  the  scale. 

CHAPTER  IV. 

The  Inversions  of  the  Common  Chord. 

Hitherto  we  have  used  our  chords  with  the  root  of  each  in  the 
bass.  This  is  the  most  simple  and  obvious  arrangement  of  the  tones, 
and  chords  in  this  form  are  said  to  be  in  the  fundamental  position. 
But  we  can  form  a  re-arrangement  of  the  tones  (for  example,  in  the 
chord  of  C),  wherein  not  the  root  but  the  third  is  in  the  bass;  and 


46 


PARKHURST  HARMONY. 


still  again,  a  second  re-arrangement  wherein  the  fifth  is  in  the  bass , 
thus: 


m 


XE 


?^ 


^   fundamental 
position. 


m 


xr 


^ 


third 
in  bass. 


33: 


xr 


^ 


fifth 
in  bas; 


XE 


The  fundamental  form  and  the  two  re-arrangements  are  still  radi- 
cally the  same ;  that  is,  they  all  have  the  same  root,  C :  but  with  this 
radical  resemblance,  they  yet  produce  quite  different  effects  from 
each  other.  These  re-arrangements  of  the  chord  are  called  its  in- 
versions.   That  in  which  the  third  is  in  the  bass 


I 


m 


» 


xx 


is  called  the  first  inversion,  that  with  the  fifth  in  the  bass  is  called  the 
second  inversion. 


8: 


^ 


The  use  of  these  derived  chords  affords  great  variety  in  the 
employment  of  the  common  chords.  Each  inversion  will  be  examined 
separately. 

The  First  Inversion. 
In  this  chord,  as  in  the  fundamental  form,  to  obtain  four-part 
harmony,  we  must  double  either  the  root,  third  or  fifth  of  the  triad, 
thus: 

^    good,     less  good.       g^^- 


XE 


-€>- 


root 
doubled 


m 


XE 


XE 


« 


third 
doubled. 


XE 


XE 


-€>- 


fifth 
doubled. 


XE 


By  a  comparison  of  these  several  forms,  and  still  more  by  ex- 
tended experience,  it  will  be  found  fnostjatisfactgryjo  double  eith^ 


CHAPTER  IV. 


47 


the  root  or  the  fifth,  and  (except  under  certain  circumstances)  least 
desirable  to  double  the  third,  i.  e.,  the  bass. 

An  explanation  must  now  be  given  of  the  figures  hereafter  to  be 
found  under  bass  notes.  The  full  figuring  of  a  chord  is  the  set  of 
figures  placed  under  a  bass  note,  indicating  the  intervals  of  the  sev- 
eral notes  from  the  bass.  Thus  the  full  figuring  of  the  chord  of  C,  in 
fundamental  position, 


i 


p 


^ 


IS 


To  simplify  the  matter,  it  is  agreed  among  harmonists  that 
when  there  is  no  figuring  with  a  bass  note,  it  shall  be  understood  that 
5  J  i.e.,  the  common  chord  in  fundamental  position,  is  intended ; 
and  when  it  is  necessary  to  indicate  a  common  chord  by  figures,  the 
full  set  is  abbreviated  to  one  or  two  of  them  as  the  case  may  be. 
This  will  be  understood  later.  The  full  figuring  of  the  first  inver- 
sion 


i 


m 


i 


XE 


3x: 


3CE 


-€3- 


jcx: 


g 

is  6  or  6  when  the  third  is  not  doubled  ;  this  is  usually  abbreviated 
to  6,  which,  placed  under  a  bass  note,  indicates  the  first  inversion  of 
a  common  chord.  This  means  that  the  root  is  a  third  below  the  bass 
note.  The  procedure  in  such  case  is,  find  the  third  below  the  bass 
note ;  this  is  the  root ;  find  the  elements  of  the  common  chord  on  the 
root,  doubling  the  root  or  the  fifth  as  the  location  of  the  voices  in 
the  preceding  chord  may  require.  Because  of  the  figuring,  this  inver- 
sion is  called 

The  Chord  of  the  Sixth. 

To  become  familiar  with  the  process  above  given,  construct  the 
following  chords,  in  each  case  doubling  first  the  root,  then  the  fifth. 

Until  we  reach  the  subject  of  ''Open  Position,"  (Chap.  VII) 
the  three  upper  voices  are  not  to  exceed  the  limits  of  one  octave; 
that  is,  the  tenor  cannot  be  more  than  an  octave  from  the  soprano. 


48 


PARKHURST  HARMONY. 


In  chords  of  the  sixth  the  soprano  and  tenor  will  often  be  just  an 
octave,  as  in  the  above  example. 


i 


XE 


33: 


-*> 


-o- 


-€>- 


XE 


33E 


6  6  6  6  6^  6 

Whether  the  root  or  the  £fth  is  to  be  doubled,  depends  upon  the 
connection ;  the  doubling  should  be  such  as  involves  the  simplest 
progression  from  the  previous  chord,  thus: 


m 


good. 

m 


s 


TV 


5» — 6 


« 


XT 


less   good*, 


XE 


3 


good 

? — r 


bad 


In  the  following  chords  of  the  sixth,  the  root  is  to  be  doubled. 

Exercises. 
3.  .  4. 


^^^rirn.>iinrriwiiJijji»ii<>jiJf4"p^a 

36"^ — 3  6\  — "a  '^5'    "   I '    b'    "   ^3'tf  ^  '^" 


In  the  following  chords  of  the  sixth,  the  fifth  is  to  be  doubled. 


m 


z. 


Exercises. 
3.       4 


"ImVfX) 


^  3'     6 


XE 


xx 


XE 


5     6*^  6^  3    $  6 

When  the  tone  that  is  doubled  in  the  chord  of  the  sixth  appears  in 
the  following  chord,  let  it  usually  he  retained  in  that  voice  which  will 
cause  the  other  voices  to  move  contrary  to  the  bass,  thus: 


s 


i 


B 


m 


H 


XE 


-O- 


« 


2Z2 


^ 


22 


good 


less  good. 


good. 


less  good. 


good 


m 


XE 


XE 


XE 


6  6  6  6  B 

The  melodic  effect  of  the  soprano  must  often  determine  the 
doubling.  In  the  following  exercises  the  pupil  is  to  use  his  own 
judgment  in  doubling  the  root  or  fifth,  observing  the  same  rules  for 
the  close  and  smooth  connection  of  chords  as  were  followed  in  all 
previous  exercises.  But  it  is  to  be  observed  that  the  "Three  Primary 
Rules"  for  the  connection  of  chords  have  their  most  particular 
application  in  the  use  of  the  chords  in  fundamental  position.    They 


CHAPTER  IV. 


49 


are  very  often,  but  not  so  invariably,  applicable  in  the  use  of  inver- 
sions. The  pupil  must  therefore  rely  a  little  more  upon  his  own  dis- 
cretion, aiming  constantly  to  secure  the  smoothest  progression  of  the 
harmony,  and  the  most  melodic  effect  of  the  soprano. 

Illustration. 


ipiti' 


±i 


^—r 6 


S^ 


XE 


t 


^ 


■^rit 


IS — 73 


^ 


221 


^ 


XE 


O      "5^ 


6  "^ 


Exercises. 


^)    \  r    -f-'^-H^-''  r    P  -  1  1    1 — r-H ii 

3    'e                            6               6                     ^               J    c     '          " 

-*?^ — —\^--f^^-'-^-p — -d— r--T — tM — II 

^  i  i-iJl-^rifi  i[^-^  N  jMj^^zJ^ 

s 


^^^ 


^ 


3X 


3       *  6        J» 


6        Hf 


g 


;^=F 


jE 


g 


331 


1 


5     6 


6. 


^ 


^ 


f 


^ 


^ 


C     "^^ 


— .^ — 


XE 


zt:^ 


7.      .      ZL 


»i: .    g 


«* HCT 


*>=^  J!rr  irnff^  irrirJMyB 


Doubling  the  Bass  Note. 

For  ease  and  smoothness  of  progression,  especially  when  two  or 
more  chords  of  the  sixth  occur  in  succession,  it  is  often  desirable  to 
double  the  bass  note,  thus: 


50 


I 


PARKHURST  HARMONY 
b. 


ij 


i 


E 


f^r 


P 


g 


xs: 


« 


XE 


^ 


9~r 


« 


g 


i 


xs: 


S 


ft  I 


6      6 


6       6    5 


(In  the  second  measure  of  (b)  the  common  chord  following  the 
chord  of  the  sixth  is  indicated  simply  by  a  5 ) . 

According  as  the  triad  from  which  the  chord  of  the  sixth  is  de- 
rived is  major  or  minor,  the  bass  note  in  the  chord  of  the  sixth  will 
be  a  major  or  a  minor  third  above  the  root.  If  it  be  a  minor  third 
the  effect  of  doubling  it  is  much  better  than  when  it  is  a  major  third ; 
and  when  minor,  no  particular  pains  need  be  taken  to  avoid  its 
doubling.  Indeed  it  is  sometimes  better  to  double  it  for  variety.  Ob- 
serve this  doubling  in  the  above  illustration. 


good 


2 


/  good. 


good. 


g 


^ — t 


?=i 


TZ. 


W} 


t 


6  ^        6       6^         6         '« 

mi.    ara    mi.    ^i^d      mi.     3ra 


If  the  bass  note  be  a  major  third  from  the  root,  it  can  be  satis- 
factorily doubled  when  the  voice  that  doubles  passes  diatonically 
through  the  octave  of  the  bass,  to  the  next  degree.  In  such  case 
the  effect  is  good.     (See  above  at  (a)  and  (b)  .) 

The  foregoing  constitute  the  two  chief  exceptions  to  the  rule 
against  doubling  the  bass  in  chords  of  the  sixth. 

In  the  following  chords  of  the  sixth,  sometimes  the  root  or  fifth 
is  to  be  doubled,  and  sometimes  the  bass  note  (the  third),  according 
to  the  rules  given  above.  These  exercises  require  careful  study  in 
order  to  become  familar  with  the  varied  treatment  of  this  chord, 
which  requires  more  care  than  any  other  chord  in  Harmony.  As 
the  variety  of  chords  increases,  there  will  be  increasing  opportunity 
for  individual  judgment  and  taste ;  therefore  let  not  the  pupil  fail  of 
constantly  having  the  sense  of  the  effect,  as  he  writes  the  exercise, 
playing  it  over  after  writing,  to  correct  any  erroneous  impression. 


CHAPTER  IV. 
Illustration. 


51 


i5 


5^ 


3f==:S: 


^ 


s 


Ztl^ 


xz: 


6 


•6    6 


6     6 


Exercises. 


i 


s 


Hi 


1         'ft    ifi 


=22 -rw 


XE 


6      6 


^^ 


?^7— <S^ 


^=?2 


^ 


^^       6 


^    ^J  jg 


^^ 


xn 


i 


f 


fi 


-€»- 


^^2 


-(5>- 


m 


6     6 


6  5 


4. 


i 


XX 


^ 


i 


^£KM^ 


XE 


-t 


3       6^6 


i 


g 


^ 


2t^ 


XE 


st:5^ 


6    '6 


6      6 


6 


The  justification  of  doubling  the  bass  when  it  is  a  major  third, 
is  found  in  the  smoothness  of  progression,  and  in  the  fact  that  the 
part  that  doubles  the  bass  has  a  decided  melodic  movement,  from 
which  it  cannot  be  turned  aside  for  the  sake  of  avoiding  the  doubling. 

Doubling  in  Unison. 

In  a  succession  of  chords  of  the  sixth,  it  is  often  advisable  to 
bring  two  voices  into  unison,  as  in  the  following. 


m 


<5}©- 


s 


zz:'7~prxi:i!g 


S 


S 


===?^^ 


s: 


S 


^ 


good. 


bad. 


^xi=:z2 


G     6 


6    6 


n:=z2 


good, 

P 


bad. 


zzz 


ISl 


-€^ 


6  6 


52 


PARKHURST  HARMONY. 


At  (a)  it  is  bad  to  double  the  ''leading  tone",  which  leaves  as 
the  best  alternative  the  bringing  of  soprano  and  alto  into  unison.  At 
(b)  the  avoidance  of  parallel  octaves  or  a  bad  doubling  of  the  bass  (a 
major  third  from  the  root)  is  also  by  means  of  a  unison.  This 
unison  of  two  voices  is  a  most  convenient  device  for  avoiding  faulty 
progressions,  and  should  be  kept  in  mind.  To  become  familar  with 
this  disposition  of  the  voices,  let  two  of  them  be  brought  into  unison 
as  often  as  possible  in  the  following  exercises,  only  not  in  two  suc- 
cessive chords. 

Illustration. 


i 


fUj4ip-|lji 


^E 


Xil 


-c^ 


2za 


^  ■&- 


m 


J3L 


TSl 


6  Q        ^    ^ 

Exercises. 


6     6 


^u^ 


i 


XE 


36 


6     6 


^. 


i 


^ 


33: 


6 


5    6 


e^ 


^ 


n 


&-^ 


m 


22=1^ 


-O- 


6        6 


m 


^ 


^m 


^ 


-o- 


$  ^ 


In  the  chord  of  the  sixth  on  the  second  of  the  scale,  either  the 
bass  note  (the  third)  or  the  fifth  must  be  doubled,  and  not  the  roj^^ 
which  is  in  this  case  the  "leading  tone". 


foot."" 


root. 


8rd 


i 


M 


5th 


Srd 


ith 


5t^ 


bad. 


bad. 


i 


good. 


good. 


good. 


good. 


good. 


m 


f 


f 


m 


r'  \r  r 


6     6        '6      6         '6      6         '6     6         6  6  "6 

In  accordance  with  the  above,  harmonize  each  of  the  following 
fragments  tzvice,  first  with  the  bass  note  doubled,  then  with  the  fifth. 


CHAPTER  IV. 


53 


^m\h(f\\¥Mkni{r\\^'^UiKfm 


6  6  6^6  6  6  6  6      "6  6  .6  6 

The  diminished  triad  (on  the  7th  of  the  scale),  which  we  found 
so  unserviceable  in  the  fundamental  position,  is  quite  effective  and 
finds  its  principal  use  in  its  first  inversion,  the  above  chord  of  the 
sixth  on  the  2nd  of  the  scale. 

There  are  unusual  difficulties  in  the  diversified  use  of  the  chord 
of  the  sixth,  and  the  pupil  is  advised  carefully  to  study  the  various 
points  above  noted,  that  he  may  be  able,  in  all  variety  of  circum- 
stances, properly  to  use  this  chord,  which,  all  in  all,  is  the  most  diM- 
cult  chord  in  Harmony. 

The  Second  Inversion. 


i 


xz: 


«^ 


i  fundamental 
postion. 


m 


XE 


XE 


^ 


second 
inversion. 


XE 


By  putting  the  fifth  of  the  chord  in  the  bass  we  obtain  a  new 
harmony,  and  yet  radically  the  same  as  the  fundamental  position  and 
the  first  inversion,  as  the  root  is  identical. 

As  in  the  first  inversion,  so  here,  we  can  double  either  the  root, 
third  or  fifth. 

best. 


I 


xc 


,  root 
doubled. 


m 


XE 


H 


third 
doubled. 


XE 


XE 


«=§= 


-e^ 


fifth  doubled. 


XE=inzi3: 


It  is  by  far  the  most  satisfactory  to  double  the  fifth  (i.e.  the  bass), 
both  in  itself  considered,  and  as  securing  a  smoother  progression  to 
the  next  chord ;  and  for  the  present  we  will  consider  this  the  only 
allowable  tone  to  double. 

The  full  figuring  of  this  chord, 


I 


"  t* 


^=^ 


m 


XEXE 


^  5 
4  4 


54 


PARKHURST  HARMONY. 


is      6        which  is  usually  abbreviated  to    J.      From  the  figuring  it 
gets  the  name  of 

Chord  of  the  Sixth-and-Fourth. 

The  procedure  in  writing  every  such  chord  is,  reckon  down  a  fifth 
from  the  bass  note ;  this  gives  the  root ;  determine  the  elements  of 
the  common  chord  on  this  root,  and  place  them  in  the  upper  voices,^ 
doubling  the  fifth  (i.e.  the  bass  note). 

It  should  be  distinctly  understood  that  figures  always  indicate  the 
intervals  of  the  upper  voices  from  the  bass  note,  and  never  from  the 
root.  This  mistake  is  often  made  by  pupils.  Thus  in  the  above 
example,  6  means  a  sixth  from  G,  which  is  E,  4  means  a  fourth  from 
G,  which  is  C,  and  G-C-E  are  all  the  diverse  elements  of  the  C-chord, 
in  the  form  of  the  second  inversion. 

The  most  common  use  of  this  inversion  is  in  connection  with  the 
common  chord  founded  upon  the  same  bass  tone : 


# 


m 


s 


«5pa^ 


35: 


XE 


T^ 


6      5 
4      3 


In  such  case  the  figures  J  must  be  followed  by  figures  that  repre- 
sent the  common  chord  in  fundamental  position,  either  I  or  5,  or  3. 
When  the  third  in  the  second  chord  is  to  be  affected  by  an  accidental, 
the  accidental  alone  is  sufficient  to  represent  the  second  chord.  If 
the  bass  moves  an  octave  in  the  last  half  of  the  measure,  no  figure  is 
necessary  over  the  second  bass  note.  (This  is  all  illustrated  in  the 
above  examples.) 

The  chord  of  the  sixth-and-fourth  is  sometimes  followed  by  a 
chord  of  the  sixth  on  the  next  degree  above. 


^m 


w 


m 


CHAPTER  IV, 
It  can  be  preceded  by  various  chords, 


55 


m 


m 


ax 


m 


XE 


b  6       5 

4 


^*^ 


^ 


?: 


2      ^ 


^— i 


^:f 


XE 


6 ^       r 


i 


^ 


xi: 


4 


No  difficulty  will  be  found  in  the  writing  of  this  chord,  if  the 
previous  general  rules  are  followed. 


Illustration. 


||EH#fH^ 


s 


3X 


XE 


^ 


g 


-5©- 


«=; 


i 


XE 


6     3 
4 


B^    (5     5 

4 

Exercises. 


^^>^-i-p4f-4 


is— f-^ 


£ 


XE 


3      6       6 


^^ 


i 


IE 


H,^  o   I  /^^ 


f 


XE 


n       6       3    6        6 
4 


3        6 
3.  4 


6      6 
4 


s 


JlJ  iMJiJ 


-^ 


i^a 


IT     6    e 

XE 


-6—8- 


rr  iPJUHrJ 


p 


TSZ 


g*  rJ  |o 


5. 


3        6    5 

4    ?l 


6       6     it        6 
4 


6      6     6      6    # 
4  4 


I 


EOE 


XE 


^^ 


Sf <2 


3      -^      ^ 


6    5      6    5       6    jg- 

4    JJ 


XT 

4    ;^ 


56 


PARKHURST  HARMONY. 


6. 


i 


22: 


7.    ^ 


? 


XE 


6 

4    3 


s 


f 


f 


f 


:^=? 


jCE 


6 
4  3 


8. 


:5F 


m 


¥ 


jCE 


6 


^ 


6 


6  4  3 

The  rule  to  retain  a  tone  in  common  in  the  same  voice  does  not 
necessarily  apply  when  a  fundamental  chord  is  in  immediate  con- 
nection with  one  of  its  inversions.  In  such  case,  the  two  chords  are 
radically  the  same,  and  there  is  no  effect  of  disconnection  if  the 
voices  change  their  position.  The  principle  is  the  same  as  in  the  case 
where  the  bass  moves  an  octave,  and  the  other  voices  can  change 
their  position  (see  page  28).  Thus  in  the  middle  of  the  second  exer- 
cise above,  a  better  effect  is  secured  by  changing  the  position  as  fol- 
lows, 


m 


«5i=^ 


5 


instead  of 


^^ 


^ 


3X 


« 


XT 


The  only  chord  of  the  sixth-and-fourth  thus  far  used  has  been 
that  whose  bass  was  the  dominant,  i.e.,  the  second  inversion  of  the 
tonic  chord.  This  is  the  most  common,  but  others  can  be  used  with 
no  more  difficulty,  and  with  good  effect. 


XlL 


t!. 


C. 


pp 


» 


^ 


XE 


XHX 


^ 


9 


<*- 


xi: 


m 


xn 


XE 


-^ 


6. 
3     4 


,e 


CHAPTER  IV, 


5i 


The  same  rules  govern  the  progression  as  heretofore.  When  any 
interval  from  the  bass  except  the  third  is  to  be  affected  by  an 
accidental,  the  accidental  is  placed  before  the  figure  expressing  the 
interval,  as  b6,  ^^.  As  an  exception  to  this  rule,  a  ^  belonging  to 
any  figure  (except  3)  is  indicated  by  a  line  through  the  figure  (as  at 
c,  above),  while  a  b  or  'i  is  placed  before,  as  at  (d).  By  some  harmo- 
nists the  accidental  is  placed  (with  less  propriety)  after  the  figure, 
6^  5#.  The  figuring  is  also  sometimes  found  above  the  bass  note, 
which  is  not  advisable,  as  it  interferes  with  the  tenor  when  placed  on 
the  bass  clef. 

Illustration. 


fe 


ZS12 


3CKZ 


m 


XE 


f 


XT 


f 


3CE 


3     4  ^      ^  H     .4 

When  there  are  two  tones  in  common  in  two  adjacent  chords, 
retain  that  one  which  will  secure  the  best  melody,  and  the  best  posi- 
tion of  the  voices,  thus : 

not. 


^ 


^^ 


^ 


m 


XE 


m 


T7      ^ 


XE 


Exercises. 


s 


^ 


'XSL 


^^^ 


f- 


XE 


6 
4   3 


m 


^ — 
4  3 


i 


551 


xc 


-6 

4     3 


^'  A 


6     6 

4 


3     ^ 


-^'rrji  r 


-cv 


4  3 


g 


5. 


3  6     6    r 


6^ 


^ 


XE 


5   6 


XE 


3  4 


g      rj 


6     6       6 


^r-27- 


-t^ 


58 


PARKHURST  HARMONY. 


^ 


& 


:3Ds: 


f 


XE 


-e>- 


5    6 


S   6 

4 


t  « 


.-^ ,,, — 


XE 


^ 


xn 


^ 


4  a 


XE 


^ 


4   ^ 


i 


6 

4    -i 


-^ 


^ 


XE 


^   6 


6 

4  a 


6       6    G 


.4  it 


Summary. 

Meaning  of  "fundamental  position"  of  a  chord : — Two  inversions 
©f  a  common  chord :— What  should  be  doubled  in  first  inversion  :— 
meaning  of  figures  under  bass  notes: — Full  figuring  of  commdn 
chord:— Full  figuring  of  first  inversion: —  Its  abbreviation: — ^The 
procedure  in  writing  chord  of  the  sixth :— Whether  root  or  fifth  shall 
be  doubled :— Which  doubled  tone  to  retain  in  next  chord : — Primary 
Rules  less  applicable  in  inversions : — Two  exceptions,  allowing  bass 
to  be  doubled : — Doubling  in  unison : — Doubling  in  sixth-chord  on 
second  of  the  scale: — Chief  use  of  tnaa  on  seventh  degree  of  the 
scale :— Doubling  in  second  inversion:—  Full  figuring,  and  its  ab- 
breviation : — Procedure  in  writing  chord  of  sixth-and-fourth : — ^^Fig- 
nres  express  intervals  from  what :— Meaning  of  ^  5  or  J  ^  or 
6  #. — Moving  all  the  voices  when  the  fundamental  position  and 
inversion  are  in  connection : — Meaning  of  accidental  before  a  figure, 
and  of  a  line  through  a  figure :— Procedure  when  there  are  two  tones 
in  common  in  successive  chords. 

CHAPTER  V. 
The  Chord  of  the  Seventh. 
We  now  come  to  the  second  elementary  chord  in  Harmony,  called 
the  chord  of  the  seventh. 


s^ 


fi=ft 


in  reality  an  outgrowth  of  the  common  triad,  formed  by  adding  to 
it  the  third  above  the  fifth,  that  is,  the  seventh  above  the  root;  hence 
called,  the  chord  of  the  seventh. 

There  is  a  peculiarity  of  this  seventh,  which  distinguishes  it 
from  every  other  tone  in  the  chord,  and  stamps  a  new  quality  upon 
all  the  chords  of  the  seventh ;  viz.,  a  strong  and  constant  tendency  to 


CHAPTER  V.  5% 

lead  downward  one  degree.  This  tendency  determines  the  progres- 
sion of  the  voice  containing  the  seventh,  and  thus  in  a  degree  con  ■ 
ditions  the  next  chord.  This  can  be  illustrated  by  the  seventh  and 
the  root,  omitting  the  other  tones  of  the  chord. 


^ 


This  inherent  drawing  of  the  seventh  introduces  a  new  quality 
into  our  chords,  illustrated  in  a  degree  by  the  leading  tone  of  the 
scale,  and  binds  together  the  harmony  more  closely  than  could  be 
the  case  in  the  use  of  only  common  chords. 

The  Resolution  of  the  Seventh. 

The  seventh,  in  its  discordance  which,  if  long  continued,  is  in- 
tolerable to  the  ear,  finds  a  point  of  rest  in  the  tone  below.  This 
leading  downward  is  called  the  resolution  of  the  seventh,  and  the 
following  chord  is  called  its  resolving  chord,  and  the  tone  below  the 
seventh  its  resolving  tone. 

The  peculiarity  of  the  seventh,  stated  above,  gives  rise  to  the  law 
The  seventh  must  always  be  resolved,  and  in  the  same  voice. 
As  the  seventh  can  be  added  to  every  triad,  we  shall  have  seven 
chords  of  the  seventh  in  the  scale : 
C  Major. 


Primary  and  Secondary  Seventh-Chords. 

The  seventh-chord  by  far  most  effective  and  most  frequently  used 
is  the  one  founded  on  the  fifth  of  the  scale,  hence  called  the  domi- 
nant-seventh-chord. This  is  so  pre-eminent  above  all  the  others  r\' 
to  be  the  one  primary  seventh-chord,  and  the  remaining  six  are  tht^ 
secondary  seventh-chords. 

The  Dominant-Seventh-Chord. 


m 


In  distinction  from  the  common  chord  it  will  be  observed  that 
every  seventh-chord  has  four  instead  of  three  diverse  tones ;  hence 
the  seventh-chord  requires  no  doubling  in  four-part  harmony. 

The  dominant-seventh-chord  can  appear  in  the  following  posi- 
tions : 


60 


PARKHURST  HARMONY. 


I 


«^ 


g 


W^ 


joe: 


m 


3X 


i>       it 


The  most  common  use  of  this  chord  is  in  connection  with  the 
tonic  chord,  which  resolves  the  seventh  of  the  dominant,  and  affords 
an  easy  progression  of  the  other  voices : 


I 


30: 


B^=«^ 


m 


jx. 


xn 


The  seventh  must  descend  (to  E)  ;  the  third  (leading-tone)  must 
ascend  (  being  in  soprano)  ;  the  fifth  (D)  has  no  decided  tendency 
Hke  the  seventh  and  the  third  (leading  tone),  and  is  to  move  in  that 
direction  which  will  result  in  the  fullest  harmony.  The  bass  can 
descend  a  fifth  or  ascend  a  fourth,  to  tonic. 

If  other  positions  be  chosen  for  the  upper  voices  the  progression 
of  the  seventh  remains  the  same,  that  of  the  fifth  and  third  may 
vary: 


^ 


^ 


^=aE 


S=5 


8 — ^tttt. 


^^ 


nsS: 


JtX. 


"     «> 


^ 


30: 


XE 


XH 


XE 


3x: 


33: 


The  third,  the  leading  tone,  when  an  inner  voice,  may  descend  if 
the  bass  ascends,  as  in  the  common  chord.  These  diflFerent  pro- 
gressions should  be  carefully  studied,  that  the  diflference  may  be 
clearly  seen. 

In  accordance  with  the  above,  harmonize  the  following,  with  the 
third,  the  fifth,  and  the  seventh  successively,  in  the  soprano,  notic- 
ing the  motion  of  the  bass,  as  that  controls  the  motion  of  the  third 
(except  when  the  third  is  in  soprano). 

(The  chord  of  the  seventh  is  indicated  by  the  single  figure  7, 
unless  other  of  the  intervals  are  to  be  affected  by  accidentals.) 
1.  2.  .  3..       _  4.     ,.  _   5. 


m 


t 


f  I"  ll^ii  r  \fW~[ 


U 


B 


XE 


XE 


'H^  I "  1 


jO- 


S 


^ 


^ 


XE 


S 


CHAPTER  v. 


t?J 


Although  every  seventh-chord,  in  itself  considered,  sounds  better 
when  all  four  diverse  tones  are  heard,  ease  and  smoothness  of  pro- 
gression, and  the  better  effect  of  future  harmonies,  often  make  it 
advisable  to  double  the  root  (no  other  tone  can  be  doubled  except 
sometimes  a  minor  third),  thereby  sacrificmj:_either^the^  tjiir^^  the 
fifth. 


F?=^ 

N-^ 

ri 

— 

t 

^^ 

-H-4t 

— j9 1 

-»-H 

t4= 

good. 

^ 

^ 

— 5  — 

bad. 

^^- 

—  O ^ 

bad. 

-f 

_5 ^__ 

good. 

-J^ 

1 

7 

i> 

LL 

h 

1" 

? 

4> 

4- 

7 

ti 

7 

^ 

It  is  much  better  to  sacrifice  the  fifth  than  the  third,  as  at  (b)  ; 
consequently, 

In  the  seventh-chord y  when  the  root  is  doubled,  omit  the  fifth. 

At  the  close  of  an  exercise  that  position  of  the  dominant-seventh- 
chord  (which  usually  precedes  the  final  chord)  is  preferable  which 
will  bring  the  soprano  upon  the  tonic  in  the  final  chord,  as  this  se- 
cures the  most  complete  effect  of  a  close ;  accordingly  in  the  follow- 
ing example,  (a)  and  (b)  are  preferable  to  (c)  and  (d)  for  a  closing 
effect. 

0.  ^        d. 


m 


m 


H 


3x: 


3z: 


good. 


^r 


« 


-O- 


3^ 


good. 


^ 


less  good. 


"ST 

least  good. 


3x: 


For  this  reason  the  following  progression  at  (a)  is  better  at  the 
close,  although  it  involves  more  motion,  whereas  the  progression  at 
(b)  is  better  at  any  other  point  of  the  exercise : 


s 


i 


b. 


3CE 


^ 


t5>- 


S 


-^ 


The  effect  is  generally  better  to  descend  than  to  asce^^d  to  the 
seventh,  eren  though  it  involve  parallel  motion  in  all  voice^i. 


6?. 


PARKHURST  HARMONY. 


The  combination  of  the  complete  seventh-chord  and  the  incom- 
plete tonic  chord  is  more  musical  than  that  of  the  incomplete  seventh- 
chord  and  the  complete  tonic  chord,  even  at  the  close  of  an  exer- 
cise, thus : 

better. 


ifihz-j         ^ 


i 


XE 


33r 


^ 


-~s^ — 

incomplete. 


incomplete. 


complete 


complete. 


XE 


XE 


jDE 


jKH 


6  7  67 

4  4 

It  is  evident  that  in  a  work  like  this  only  the  most  general  state- 
ments can  be  made.  The  pupil  must  seek  to  obtain  the  best  efTects, 
not  by  slavishly  following  the  rules,  but  by  consulting  to  a  degree 
his  own  taste,  thus  quickening  his  musical  sense.  An  exercise  may 
be  correctly  written,  and  yet  produce  a  monotonous  impression.  This 
is  generally  caused  by  too  little  motion  in  the  soprano,  thus : 

better. 


I 


3X 


W^ 


« 


«a- 


iS 


^^ 


^r 


W^ 


■si-zf- 


m 


jS 


3H 


XE 


^6  7  6  7 

In  working  out  the  following  exercises,  the  seventh-chord  having 
been  written,  the  first  thing  to  do  in  the  following  chord  is,  to  write 
the  note  that  resolves  the  seventh  in  the  same  voice  in  zvhich  the 
seventh  occurs,  then  move  the  other  voices  to  their  proper  places. 

Illustration. 


m 


^ 


^ 


ixr: 


2=12 


Z?=^ 


«: 


:gr-" 


■6f-  -&- 


% 


jCE 


tr: 


%     3 


CHAPTER  v. 
Exercises. 


63 


§ 


xc 


3      6       7 


6  6 

4   3 


XE 


3   6 
4 


6      6 


^1>    I  J  II  ilJ  J 


F  If  ^  k^  r 


4. 


fi       tt       6 


^ 


iss: 


-^TJ    T-^  i^if 


5. 


6    7 
4 


-o- 


XE 


f 


iS>— ^ 


6^ 


6       7 


6      7 


6. 


-^ 


f 


33C 


XE 


Ff=ff 


4  3 


6 

4   ^ 


6     7 
4 


f 


i 


zz 


-^ 


6    '6 


4     7 


^^ 


^^ 


S 


t5« «• 


jS. 


5  B 


0. 


»^ 


i 


^ 


7  H    7       -»- 

4 


-o- 


"B  6 


#       6 


^ 


XE 


^ 


XE 


2Z 


XH 


6  6 

4  ;i 


6     7 
4 


The  Dominant-Seventh  in  the  Minor  Scale. 
in  A  minor. 


^^^^^ 


m 


m 


«M> 


iJ^gr 


^==« 


^^   O 


S 


XE 


XE 


XX 


XE 


XE 


XE 


XX 


>v4» 


*In  this  measure  write  two  positions  of  the  same  chord,  to  as  to  maintain  the  movement 
in  half-notes. 


^ 


PARKHURST  HARMONY, 


As  will  be  seen  above,  the  progressions  are  identical  with  those  of 
the  dominant-seventh  in  the  major  scale,  and  require  no  further 
-explanation. 

Illustration. 


m 


Wf 


XE 


§ 


«5F 


7  '  tf 


XE 


22 


*t  n 


^^  « 


6     5 


f    ' 


(It  is  best  that  the  voice  having  the  8  should  take  the  7,  as  in 
the  last  measure  but  one  of  the  illustration.) 

Exercises. 


:««: 


i 


pip\f'  r 


^ 


XH 


6 

4    j* 


8    7 


*ir 


<o  I  r^ 


f 


w 


jDC 


t-' 


^ 


g 


6    7 

4   ff 


XE 


6         '#     ^ 


TT-yy-f- 


-^ 


4. 


^ 


^ 


o- 


^HS 


3    6       j*    6 


6     6       ^7 

4  4    ^ 


Summary. 

Formation  of  the  seventh-chord : — Peculiarity  of  the  seventh-in- 
terval:— Resolution  of  the  seventh: — Primary  and  Secondary  sev- 
enth-chords:— Difference  between  common  and  seventh-chords  in 
doubling: — The  commonest  progression  from  dominant-seventh 
<:hord: — Figuring  of  seventh-chords: — When  doubling  is  advis- 
able:— What  shall  be  doubled  and  what  omitted: — Better  descend 
then  ascend  to  seventh: — Complete  dominant-seventh,  followed  by 
incomplete  tonic  chord : — Monotony  of  exercise  due  to  what : — Re- 
solving seventh  in  the  same  voice. 


CHAPTER  VL 


65 


CHAPTER  VI. 
The  Inversions  of  the  Dominant-Seventh-Chord 
In  C  major 


in  A  minor 


^ 


-4i 


&, 


"o     o«»    gX 


^ 


s 


6  (6\  6  6742Y 


:i) 


§ 


^ 


#»»(>!!■> 


-o- 


6/6\  -%- 
5V5^  4 
a  3 


Jr\2) 
2 


The  dominant-seventh  has  three  inversions.  The  first,  formed  by 
putting  the  third  in  the  bass,  has  for  its  full  figuring  5 ,  abbrevi- 
ated to  |,  hence  called 

The  Chord  of  the  Sixth-anekFifth. 

In  the  different  positions  as  follows : 
in  C  major 


in  A  minor 


XT 


^ 


«: 


B^ 


no    o 


-«*• 


i 


« 


3?o; 


-«»- 


■O    o 


^o    " 


^ 


-!■>        t> 


xx: 


XE 


The  process  in  writing  a  chord  of  the  sixth-and-fifth  is,  ^rj/  y?na 
//»^  roo^  (a  third  below  the  bass  note)  ;  on  the  root  construct  a  sev- 
enth-chord, so  disposing  the  notes  that  the  voices  will  move  properly 
from  the  preceding  chord.  As  a  preliminary,  write  the  following 
chords  of  the  sixth-and-Hfth  in  the  different  positions : 


66 


PARKHURST  HARIl/iONY 


First  inversion  of  dominant-seventh  in  major  scales. 


^^ "  Ph^  W^^Mihk^m ..  Whhh 


M 


m 


s 


JDE 


S 


3x: 


ri,o  iin,"    4fe 


fe^ 


XE 


XE 


First  inversion  of  dominant-seventh  in  minor  scales. 


prjjo||i>i|.jiVhl|i/)>,jluioik^^y^^oll^ 


ttKmi: 


The  second  inversion,  formed  by  putting  the  fifth  in  the  bass,  has 
for  its  full  figuring  4^  abbreviated  to    ^,  hence  called 

The  Chord  of  the  Fourth-and-Third. 
In  its  different  positions  as  follows : 
in  C  major 


I 


tj: 


30^: 


^^^=^ 


5 


xy 


m 


■^ 


in  A  minor 


#Ro#8    jt 


JOSS 


g«jffo*> 


«»■ 


§ 


4 
8 

The  process  in  writing  this  chord  is,  find  the  root  (a  fifth  below 

the  bass  note)  ;  on  the  root  construct  a  seventh-chord,  disposing  the 
notes  as  the  previous  chord  requires.  Write  the  following  chords  of 
the  fourth-and-third,  in  the  different  positions : 

Second  inversion  of  dominant-seventh  in  major  scales. 


'r>^KA\h-\\hL  M-\\W..\\m^ 


X3E 


^:? 


S 


^ 


g 


^ 


jci: 

4 
3 


CHAPTER  VL 

Second  inversion  of  dominant-seventh  in  minor  scales. 


67 


jer      ^  J^  j^  J^         &■  ^  q6 


-6- 
4 
3 


4 
3 


-6- 
4 
3 


1 

3 


XE 


3 


The  third  inversion,  formed  by  putting  the  seventh  in  the  bass, 
has  for  its  full  figuring     4      abbreviated  to  2,  hence  called 


The  Chord  of  the  Second. 
In  its  different  positions  as  follows: 
in  C  major 


i 


r^ 


»V    o 


§ 


Xft. 


8    8    « 


"O" 


■o- 


in  A  minor 


I 


iB^ 


<>8  {ts-m- 


The  process  in  writing  this  chord  is,  first  find  the  root,  (a  seventh 
below  the  bass  note)  ;  on  the  root  construct  a  seventh-chord,  dispos- 
ing the  notes  as  the  previous  chord  requires.  Write  the  following 
chords  of  the  second,  in  the  different  positions : 

Third  inversion  of  dominant-seventh  in  major  scales . 


^y-^..\\\:'\mK  pfy°  p,i^^^  *^^ 


*5F 


m 


XE 


2FF 


Tn 


^ 


a 


^ 


S 


17-rr 


Jtxi: 


^^ 


^ 


2  2  2  2 

Third  inversion  of  dominant-seventh  in  minor  scales. 


^ 


i,  .>  \\U      Pi? 


-^ 


XH 


^''<^rrhv 


^^m 


2 


4- 
2 


A- 
2 


2 


'I 


68 


PARKHURST  HARMONY. 


It  wijl  assist  the  memory  to  notice  that  the  figures  follow  in  regu- 
lar order  from  7  downward,  thus, 

fundamental  form 7 

first  inversion 6 

second       **     | 

third         "     2 

The  figuring  of  the  inversions  must  be  well  memorised,  to  pre- 
vent any  confusion  among  themselves,  and  to  keep  them  distinct  from 
the  inversions  of  the  common  chord.  The  common  chord  with  its 
inversions,  and  the  seventh-chord  with  its  inversions  can  be  compared 
as  follows: 


m 


-*>- 


m 


4 


« 


€^ 


« 


^ 


That  tone  v/hich  in  the  fundamental  position  is  the  seventh  has 
precisely  the  same  tendency  to  lead  downward  in  all  the  inversions. 
Accordingly  we  speak  of  that  tone  which  is  seventh  in  the  funda- 
mental position  as  still  the  seventh,  whatever  the  inversion.  Thus 
in  the  following  four  chords  F  is  equally  the  seventh  in  all  of  them. 


i 


^ 


a^ 


-CV: 


«^ 


XT 


m 


and  the  resolution  of  that  tone  is  the  first  thing  to  be  attended  to 
in  the  following  chord.  B  is  also  called  the  third  in  all  of  them,  and 
has  a  constant  tendency  (as  leading  tone)  upward  to  C.  Similarly 
G  is  the  root,  and  D  is  the  fifth  in  them  all.  This  uniform  method 
of  designating  the  tones  of  the  chord  serves  to  keep  constantly  in 
mind  the  derivative  nature  of  these  new  harmonies,  and  simplifies 
the  progression  of  the  voices,  by  finding  them  so  largely  the  same  as 
in  the  fundamental  form. 

In  the  fundamental  form  we  frequently  find  it  necessary  to  double 
the  bass  and  to  sacrifice  the  fifth  (rarely  the  third).  In  the  inversions 
there  is  no  doubling,  consequently  no  sacrifice  of  any  element  of  the 
chord.    Each  inversion  must  contain  all  four  elements  of  the  chord. 


CHAPTER  VI. 


69 


From  the  foregoing  we  are  now  able  properly  to  resolve  all  three 
inversions.  The  various  positions  of  the  three  upper  voices  can 
cause  no  difficulty  when  the  true  character  of  these  chords  is  under- 
stood. 

Dominant-Seventh  Inversions  in  C  major. 


-o- 


g 


^ 


xr 


XE 


« 


XE 


—  <M>     =:^^<K 


» 


^ 


-€>- 


"or 


§ 


5F 


r     <» 


-o- 


XE 


XE 


6  2         6 


Dominant-Seventh  Inversions  in  A  minor. 


^^ 


o     t 


^^ 


1^ 


X3: 


^ 


■<€!€> 


^ 


XE 


==xi: 


^^ 


-^ 


3CE 


XE 


XE 


6 
5 


XE 


xx: 


1¥ ^—^ 

2 


j6- 

4 

3 


K       *^ 


i4- 
2 


(Let  it  be  remembered  that  figures  express  the  intervals  from  the 
actual  bass,  not  from  the  root,) 

Although  it  is  generally  better  to  descend  to  the  seventh. 


m 


H 


m 


XE 


^ 


better. 


ijpP= 


XX 


8     7 


8      7 


yet  it  is  sometimes  better  to  ascend,  when  a  decidedly  melodic  move- 
ment can  thereby  be  attained,  thus: 


^M 


S 


iV  " 


i 


XX 


S|     6     6 
4      5 


70 


PARKHURST  HARMONY. 


Illustration. 


3^ 


u 


a3=t 


z? 


25=5 


-«*■ 


m 


"t  6   7 


XE 


Exercises. 


551 


i 


f 


XE 


5      6 


2. 


i 


^izz 


g 


f 


xk: 


^-^ 


^ 


2    6 


3. 


m 


^v 


22 


f 


-O- 


8  7 


Is 


6 

4    7 


^ 


f 


-e^ 


6    2.6 


m 


8    7 


35: 


6     7 
4 


''M:iJjif[iiii  ii-g 


6     Te" 

5 


-e-     6 


3    6 
8.  5 


^^fc 


m 


6  7 


6        6 
4 


^ 


6    '6       "4 

4        3 


o: 


ft  7 


i 


A^     '6 


^=22 


^^ 


4 
41 


CHAPTER  Vll. 


71 


9. 


51l=fi 


32 


6  -^      *' 


O- 


6  7 
4 


3      « 


10. 


m 


^ 


f 


yfe 


6  ^ 
4 
3_ 


4    1 


i 


i 


^ 


EXE 


12. 


6       6   2       6 
4 


6    7 


o       It  »^ 


■^ 


xr 


1^    3       6 


Summary 

Name  of  first  inversion  of  a  seventh-chord,  its  full  figuring  and 
abbreviation: — Procedure  in  writing  chord  of  sixth-and-fifth : — 
Name  of  second  inversion,  full  figuring  and  abbreviation: —  Pro- 
cedure in  writing  it: — Name  of  third  inversion,  full  figuring  and 
abbreviation  : — Procedure  in  wTiting  it : — Order  of  figures,  from 
fundamental  to  third  inversion : — The  same  tone  to  be  regarded  as 
seventh,  in  fundamental  position  and  in  all  inversions: — The  law  in 
all  inversions  as  regards  doubling: — Sometimes  ascend  to  seventh 
for  melodic  efifect. 

CHAPTER  VII. 

Close  and  Open  Position.     Concealed  Fifths  and  Octaves. 

Score.     Cross-Relatiox.     Sight-Reading. 

Thus  far  all  our  exercises  have  been  written  with  the  three  upper 
parts  as  closely  together  as  possible.  As  a  result  these  three  voices 
have  always  been  ivithin  the  limits  of  an  octave. 


m 

M=^ 

u,   r-  ■- 
-9— i? — 

t- 

-^o — 

4» 

^    7 

Chords  written  in  this  manner  are  said  to  be  in  close  position,  which 
is  the  easiest  manner  of  writing  for  the  beginner.  But  it  is  evident 
that  a  permanent  limitation  of  these  three  voices  to  the  compass  of 
an  octave  would  eventually  produce  monotony,  and  the  best  effect 
can  often  be  secured  only  by  spreadin^^  tJiese  voices,  and  the  harmony 


72 


PARKHURST  HARMONY. 


is  said  to  be  in  open  position  when  the  three  upper  voices  do  not  fall 
within  the  limit  of  an  octave,  thus : 

I 


I 


m 


9-^ 


a 


XE 


m 


6  7 

(It  will  be  seen  that  the  above  harmony  is  identical  with  the  pre- 
ceding example,  the  only  difference  being  that  the  voices  are  spread). 

The  octave  is  the  boundary  line  between  close  and  open  position,, 
and  soprano  and  tenor  being  in  octave  we  may  call  the  position 
either  close  or  open.  It  is  to  be  understood  that  the  alto  must  always 
lie  between  soprano  and  tenor: — that  is,  the  parts  are  not  to  cross 
each  other.  An  octave  or  less  between  soprano  and  tenor  makes 
close  position.  An  octave  or  more  between  soprano  and  tenor  makes 
open  position. 

The  acquirement  of  facility  in  open  position,  and  at  the  same 
time  a  review  of  the  subject  up  to  this  point,  is  the  object  of  the 
following  sets  of  exercises,  covering  the  several  points. 

Attention  must  be  called  to  two  matters :  first,  it  is  never 
allowable  for  any  two  adjacent  voices,  except  the  tenor  and  bass,  to 
be  distant  from  each  other  more  than  an  octaz^e,  as  it  invariably  pro- 
duces a  thinness  of  effect,  which  is  never  agreeable,  thus: 

£ft- 


m 


K. 


^ 


m 


bad. 


ax 


XE 


gooct. 


This  prohibition  does  not  avail  in  the  case  of  tenor  and  bass,  but 
it  is  better  even  in  this  case  that  the  interval  should  not  too  largely 
exceed  an  octave. 


^ 


3 


^ 


i 


g 


XT 


n 


better. 

(2_ 


I 


-€V- 


IDT 


Secondly,  the  pupil  must  be  on  his  guard  against  parallel  fifths, 
which  are  more  likely  to  occur  in  open  than  in  close  position.  Thus 
the  following,  in  close  position, 


CHAPTER  VIL 


73 


¥ 


zz: 


^ 


XEDE 


3x: 


6 

when  put  into  open  position,  as  at  (a),  shows  parallel  fifths ;  it  must 
therefore  be  arranged  as  at  (b). 

a.  b. 


i 


m 


&. 


331 


XE 


m 


XE= 


3s: 


Two  voices  can  move  diatonically  from  a  perfect  to  a  diminished 
fifth,  but  not  from  a  diminished  to  a  perfect  fifth,  thus: 


Xi. 


-o- 


-€>- 


:£t 


-o^ 


JQL 


H 


-O^ 


good; 


-Ci- 


j5I 


good 


«  1 


.^fc^ 


^ 


J  J-r^  I,  J  'J" 


XE 


^ZSTL 


351 


-C^ 


-O- 


O- 


i:i 


better. 


bad. 


'6     I4 


XE 


1       '4  6      ^       ^ 


XE 


XH 


The  progression  from  a  diminished  to  a  perfect  fifth  is  neverthe- 
less sometimes  so  inconspicuous  as  to  be  used  even  by  good  writers, 
especially  when  it  occurs  between  alto  and  tenor,  thus. 


F^ 

2-" 0 [-.r^ 

y 

—  — ^ 

but  in  general,  the  prohibition  is  valid. 


74 


PARKHURST  HARMONY. 


Note.  A  word  of  explanation  in  regard  to  the  coriect  notation 
of  exercises  in  open  position. 

The  stem  of  a  note  should  be  so  placed  as  to  bring  it,  as  much 
as  possible,  upon  the  staff.  If  the  note  be  above  the  middle  line, 
the  stem  should  be  turned  down,  if  belozv  the  middle  line,  it  should 
be  turned  up.  If  two  or  more  notes  average  above  the  middle,  and 
are  joined  by  one  stem,  it  should  be  turned  down  ;  if  they  average 
below  the  middle,  it  should  be  turned  up. 


m 


^ 


g 


^Eip^ 


?= 


In  "close  position,"  the  three  upper  voices  are  commonly  joined 
by  one  stem,  on  the  soprano  staff.  But  in  "open  position,"  soprano 
and  alto  are  written  on  the  upper  staff,  and  the  tenor  is  commonly 
placed  on  the  bass  staff.  In  this  case,  each  pair  of  voices  can  be 
united  by  a  single  stem,  as  above,  or  each  voice  can  have  a 
separate  stem,  in  which  case  the  soprano  and  tenor  stems  must  be 
turned  up,  the  alto  and  bass  stems  turned  down,  thus : 


s 


u 


± 


i 


W 


fi" 


Pf 


F3 


i 


^ 


JJ 


i 


m 


% 


g 


XE 


2=22 


F 


T5- 


The   same   laws   prevail   in   the   connection  of  chords   in  open 
as  in  close  position.     Let  the  illustrations  be  carefully  examined. 
Primary  Common  Chords. 
Illustration. 


I#=f^ 

Ip    P     1 

'J 

4> 

t4= 
^- — 

—  9 — 



5> — 

-€»- 

^      r 

1^ 

*» 

or  last  two  chords  thus. 


i 


XE 


m 


XE 
XE 


Major. 


m 


CHAPTER  VII 

Exercises. 
2. 


75 


^ 


an 


22 


3X 


3 


XC 


g 


^ 


XE 


«^ ^ 


5. 


m 


6. 


7. 


2z^ 


6^^ 


-6 

"Minor, 
1. 


«F 


3. 


P^ 


P33 


S 


S=a 


XE 


XT 


3      4 
5 


« 


^^ 


rj    g^ 


r  'm'  iJj  n 


8. 


K.JlrJliJ 


^ 


& 


m 


s^«^ 


5       ?  '^        ^  3  I, 

Concealed  Fifths  and  Octaves. 


Before  proceeding  further  in  exercises  in  open  position,  it  is 
desirable  to  explain  a  progression  which  is  of  frequent  occurrence, 
under  some  circumstances  productive  of  one  of  the  worst  effects 
in  Harmony,  under  others,  perfectly  permissible.  This  progression 
is  that  of  a  concealed  fifth  or  a  concealed  octave.  (The  fifths  here 
spoken  of  are  only  the  perfect  fifths). 

A  concealed  Hfth  occurs  if  two  voices,  at  any  other  interval  than 
a  fifth,  progress  in  parallel  motion  to  a  perfect  fifth,  thus: 


i^^ 


^S^^ 


r—i»    l8   *y    1  **^ 


"cr 


3X 


xn 


xy- 


XE 


^€> 


XT— -^ 


§ 


^V  — o 


-<e»- 


-et- 


-€^ 


JCK 


Af     O 


;z^ 


XX 


Concealed  fifths  may  exist  between  any  two  voices  in  the  har- 
mony.    To  make  sure  of  this  progression  being  perfectly  under- 


76 


PARKHURST  HARMONY. 


stood,  let  the  pupil  add  another  voice  to  the  one  given  below,  in- 
volving the  progression  of  concealed  fifth. 


$ 


g 


XE 


XX 


n^ 


IE 


XE 


XI 


XX 


add  the  second  voice  below.  ^dd  the  second  voice  above. 

Similarly,  a  concealed  octave  occurs  if  two  voices,  at  any  other  in- 
terval than  an  octave,  progress  in  parallel  motion  to  an  octave,  thus 


.^€^  l«» 


xi: 


xr 


-^ 


xc: 


_Ol. 


O     ' 


o 


SEE 


xr 


XE 


30: 


i 


Xfl 


JCM- 


-0«r 


tf   o 


<r^ 


m 


3CE 


XH 


-^ 


XE 


Add  another  voice  to  the  one  given  below,  involving  the  pro- 
gression of  concealed  octaves. 


SOE 


XT 


O 


XE 


♦>- 


3CE3XI 


^^ 


3D|g;=^ 


Qq  lf> 


XE 


add  voice  above. 


add  voice  below. 


Let  the  pupil  find  all  the  concealed  fifths  and  octaves  in  the  fol- 
lowing, comparing  each  pair  of  voices. 


|i|.(:i.ijiJriiTir[irpJ.iiijij 

^  =  E-5=^  =  E^-:5^^=c^^5=^^=t^l 

There  is  perhaps  nothing  in  Harmony  in  regard  to  which  it  is 
more  difficult  to  give  rules  than  concerning  concealed  fifths  and 
octaves.  Certain  it  is  that  text-books  and  teachers  in  general  make 
too  much  ado  over  them,  so  that  they  become  a  perfect  bugbear  to 
the  pupil.  The  difficulty  of  the  case  is,  that  while  many  of  these 
concealed  fifths  and  octaves  are  inadmissible,  a  large  number  of 
others  are  admissible,  and  even  unavoidable,  and  it  is  impossible 
to  make  any  plain  and  simple  classification  of  the  good  and  the  bad. 
After  all  that  shall  be  said,  much  must  still  be  left  to  the  musical 


CHAPTER  VII. 


17 


instinct  to  determine  the  propriety  or  impropriety  in  many  individual 
cases. 

The  usual  explanation  of  their  bad  effect  is  as  follows ; 
when  a  voice  moves  by  a  skip,  the  intervening  tones  are  more  or  less 
faintly  suggested.     Thus  in  the  following, 


concealed  fifths- 
a.  b. 


c. 


d. 


e. 


^^ 


<v 


t»    H¥ 


XE 


"         O 


» 


iF-Q^ 


Ten 


JK=^ 


jCH 


xe: 


T^-^ 


concealed  octaves. 
a.  b 


*  ♦  C»  '  O" 


XE 


XTT 


XlL 


XE 


-TT- 


uc®: 


XE 


:m^t 


the  black  notes  are  those  that  intervene  in  the  skip,  and  the  last 
intervening  note  forms  a  fifth  or  an  octave  with  the  other  voice,  fol- 
lowed by  the  expressed  fifth,  or  octave.  The  first  fifth  or  octave  be- 
ing  suggested  in  the  above  manner,  and  the  second  being  expressed^ 
it  results  in  a  concealed  sort  of  parallel  fifths  or  octaves,  hence  the 
name,  concealed  fifths  and  octaves.  Once  more  let  it  be  said  that  the 
''concealed"  fifth  or  octave  is  not  the  one  that  is  actually  existent 
and  audible,  but  the  one  that  lies  between  an  expressed  and  an  un- 
expressed, or  between  two  unexpressed  tones.  It  is  imagined  rather 
than  heard,  and  is  thus  in  a  sense  ''concealed." 

The  fallacy  in  the  foregoing  explanation  is,  that  those  cases 
in  which  both  voices  make  a  skip,  (and  accordingly  both  tones  of  the 
first  fifth  or  octave  are  only  suggested,  as  at  (e)  above),  are  the  most 
objectionable;  and  on  the  other  hand,  those  cases  in  which  one  voice 
moves  by  a  degree,  (and  so  the  first  fifth  or  octave  is  most  evident,, 
by  having  one  of  its  tones  actually  expressed,  as  at  (a),  (b),  (c),. 
(d),  above),  are  the  most  admissible.  But  we  are  not  concerned 
here  with  the  philosophy  of  the  matter,  particularly  as  the  philosophy 
is  so  decidedly  "concealed ;"  our  purpose  is  fulfilled  in  helping  the 
student  as  far  as  possible  to  determine  what  to  avoid  and  what  to 
permit.  Whatever  the  explanation,  the  fact  remains  that  no  chord  is 
fully  satisfactory  in  which  the  fifth  or  the  octave-relation  of  any  twa 
voices  is  made  unduly  conspicuous ;  and  it  is  made  more  or  less  con- 
spicuous by  the  progressions  called  "concealed  fifth  and  octave."  It 
is  most  conspicuous  when  both  voices  make  a  skip: 


$ 


XE 


XE 


""l"ol"o 


XE 


XE 


-O- 


78 


PARKHURST  HARMONY. 


less  conspicuous  zvhen  only  one  voice  skips: 


i 


EE^ 


^ 


ISJL 


more  conspicuous  between  the  outer  voices: 
fifth. 


octave. 


less  conspicuous  between  outer  and  inner,  or  two  inner  voices. 


$ 


■^ 


o- 


<e>- 


<^ 


-4^ 


xi: 


« 


XI 


Oi»    I  JKT^ 


^ 


-^>- 


XH 


8: 


XE 


OC^ 


xr^ 


O    .     ^<; 


Srcfi 


£2. 


» 


o: 


-€>■ 


XE 


TOE 


■^^ 


The  most  detailed  classification  that  could  possibly  be  made  would 
still  require  many  exceptions,  and  be  all  too  burdensome  to  the 
memory.  To  simplify  the  law  to  practical  limits  it  may  be  stated 
as  follows : 

Concealed  fifths  and  octaves  are  most  to  be  avoided  between  the 
outer  voices,  but  are  allowable  in  the  case  of  any  two  voices,  when 
either  of  the  tzvo  moves  only  one  degree  (best  of  all  zvhen  the  single 
degree  is  a  semitone),  thus: 


or  in  the  case  of  the  tzvo  inner  voices  zvhen  both  skip,  the  combined 
progression  of  all  four  voices  being  good. 

The  above  rule  is  the  best  general  statement  of  the  case.  But  it 
is  not  offered  as  being  infallible ;  it  only  admits  of  fewer  excep- 
tions than  any  other.  The  proper  observance  of  the  Three  Primary 
Rules  for  chord-connection,  and  particularly  contrary  motion  be- 
tween the  three  upper  voices  and  the  bass,  will  largely  eliminate  the 
objectionable  cases.  There  are  two  exceptions  to  the  general  rule 
that  require  notice. 


CHAPTER  Vn. 


79 


First :  Concealed  fifths  and  octaves,  in  which  both  voices  skip, 
can  occur  even  between  the  outer  voices,  when  the  progression  of  the 
harmony  is  from  one  position  to  another  of  the  same  chord,  or  from 
an  inversion  to  its  fundamental,  or  vice  versa,  thus : 


«y-^ 


o 


-^^    1^^-^ 


3x: 


^>- 


xn 


o  o 


o   c» 


«: 


»  o    U»  fg 


xr 


W 


XE 


fi: 


^ 


SA 


ii_ 


XKX 


<>    €f 


XE 


XE 


XE 


;r 


;z: 


<^^ 


4      — 


6    - 
4     - 


6      7 
5 


Second :    Concealed  octaves,  in  which  one  voice  moves  only  one 
<legree   cannot  occur,  if  the  voice  thus  moving  contains  the  discord 

of  the  sevenih  and  its  resolution,  thus: 


a.  bad. 


XE 


b.  good. 


XE 


€^0 


XE 


^^ 


« 


3331 


3DC 


^m 


-o^ 


ffi 


-o- 


3^ 


ja. 


<ir 


^ 


3t3E^ 


a- 


^  b 


o_ 


^ 


^O-O-     iOO 


^ 


i 


XE 


XE 


2^ 


XE 


XE 


It  will  be  seen  that  the  fault  in  the  above  example  will  always  be 
avoided  by  following  the  first  of  the  Three  Primary  Rules, 

Concealed  Unisons. 


h-Jt—  STiftui 

rS^^ 

^=^^OT 

f^sq 

=?^ 

^ 

1-"^ 

l?^* 

o 

#8^ 

iJ 

■ 

t^^ 

These  are  of  the  same  nature  as  concealed  octaves,  but  with  worse 
eflFect,  and  entirely  inadmissible  between  soprano,  alto  and  tenor. 
Between  tenor  and  bass,  they  are  less  objectionable,  but  contrary 
motion  into  the  octave  is  usually  preferable. 

The  above  points  concerning  concealed  fifths,  octaves,  and  unisons 
need  to  be  thoroughly  understood  and  borne  in  mind  in  writing  all 
future  execises.  Conscious  effort  zuill  ultimately  result  in  uncon- 
scious compliance  zvith  all  rules. 


80 


PARKHURST  HARMONY. 

Secondary  Common  Chords. 
Illustration. 


iU^h^'lymf^\[\'\fU"i 


zr;# 


I*-     i»- 


m 


XE 


Exercises. 


Open  position. 


?l? 


^m 


XI 


&)     'g' 


2. 


^ 


r  ir  -J  i^r  '^-^  'r  r  '-^  r  'oi 


« 


^ 


? 


3x: 


zt^ 


ztz^ 


4. 


i 


S 


^ 


ax 


V 

5.     5 


^ 


w— 1& 


FT-<^ 


-€V 


6. 


s 


•w- 


5 


^ 


^ 


3    - 


Inversions  of  the  Common  Chord. 
Illustration. 


^ 


XE 


-♦>- 


pp=« 


iCEEt 


P 


s 


^ 


firn-T 


r 


xr 


6 
4     3 


CHAPTER  VII. 


8? 


An  incomplete  chord  (as  in  the  6th  measure)  can  be  allowed 
when  a  much  smoother  progression  of  the  voices  is  thereby  at- 
tained.    (Similarly  in  exercise  (2)  at  *.) 


Exercises. 


'k    Open  position. 


')-.!  h  M.l 


i 


zznie 


^ 


3X 


6        6 
4  3 


m^ 


3. 


i 


*^ 


ujifi;iJjMfii;i^^ 


i 


33: 


3         TTg 


4     ^ 


^^ 


-o- 


6^ 
4 


l» 


C3 

I3 


The  Dominant-Seventh  Chord. 
No  further  illustration  of  open  position  is  necessary, 

Exercises. 

Open  position . 
1. 


^ 


3L 


ax 


6, 


<v 


6    6 
4 


6  7 


2. 


g 


75-iS^ 


n: 


jitnm  iLjujp 


XH 


S       ^6 
3.  * 


6    6      8   7 
4  # 


g 


^ 


j  UJiv   ifi  'oM^^ 


t)  7    '  O 


3        6 


t. 


^ 


fe 


^ 


^ 


zc 


m 


6 

4  a 


6  6  7 

4 


82  PARKHURST  HARMONY. 

Inversions  of  Dominant- Seventh. 
Exercises. 


Open  positioa. 


SS 


^ 


I 


I 


i 


BEE 


22 


6    T- 

4  8 


zz 


^ — 
»      5  ' 


3     2        6 


«6 


^ 


Jl'^flf^rir  J  Ijj  I-Jjljjl"^ 


6       67 

4 


■Mil  H  J, I  If  J  i;  ij  iii.iujLi^a 

■aft  »    '  eaf^^T  e    Vi 


^ft 


r  If  r  ir  ^J  If  J  III  hr  Ir^^ 


5. 


^ 


^ 


6    6 
4- 


i 


f? 


^^ 


6. 


5     "6 
5 


*    I 


m 


i 


IT 

6  87 


? 


^^ 


-O- 


^  r? 


It     '6     -^ 
4 


87 


Writing  in  Score. 

A  composition  is  said  to  be  written  "in  score"  when  each  voice 
or  part  is  written  on  a  separate  staff.  The  score  may  contain  as 
many  staves  as  there  are  voices  performing  simultaneously,  even 
up  to  twenty  or  more,  as  in  an  elaborate  orchestral  composition. 
Writing  "in  score"  has  nothing  to  do  with  close  or  open  position. 
Each  staff  must  have  its  proper  clef  prefixed.  It  is  customary  in 
this  country  to  use  the  same  clef  for  tenor  as  for  soprano,  with  the 
understanding  that  as  used  for  the  tenor,  the  pitch  is  an  octave 
lower  than  as  used  for  soprano.    Accordingly  the  following 


i 


I: 


m 


-o- 


CHAPTER  VII. 


a3 


when  written  "in  score''  would  appear  thus : 


The  clef  in  general  use  for  soprano,  alto  and  tenor,  as  above,  is 
really  the  violin  clef.  In  Germany,  these  three  voices  are  still 
written  to  some  extent,  on  different  clefs,  belonging  specifically  to 
soprano,  alto  and  tenor,  in  each  of  which  C  has  a  different  location. 
These  old  clefs,  once  in  general  use,  are  now  rarely  employed  in 
vocal  music,  although  the  alto  clef  is  constantly  used  for  the  viola, 
and  the  tenor  clef  sometimes  for  the  violoncello,  in  orchestral  music. 
Thorough  musicianship  requires  familiarity  with  the  tliree  old  clefs, 
but  as  the  large  majority  of  Harmony  students  do  not  carry  their 
studies  far  enough  to  require  this  knowledge,  it  is  not  advisable  to 
impose  upon  all  the  labor  of  learning  them. 

For  the  sake  of  the  few  who  will  need  the  information,  the  fol- 
lowing explanation  of  the  old  clefs  is  given,  and  it  is  advised  that 
prospective  composers  should  become  familiar  with  them  by  adopt- 
ing their  use,  to  some  extent,  in  future  exercises  of  Harmony.  This 
matter  will  be  left  to  the  discretion  of  the  individual  pupil. 

The  soprano,  alto  and  tenor  clefs  are  given  below,  with  the  scale 
in  each  that  exactly  corresponds  with  the  scale  of  C  in  the  violin 
clef. 

The  same  C  is  indicated  in  the  four  clefs,  thus: 


i 


lib  ^ 


o- 


-o- 


04 

Violin  clef. 

Soprano  clef. 
Alto  clef. 

.Tenor  clef. 


PARKHURST  HARMONY. 


w 


i 


"cr 


xi: 


-€> 


if       o 


3n: 


XE 


31: 


o      ** 


xs: 


1 


xn 


XE 


-€>- 


Xfe. 


.Ol 


i 


-o- 


«1     o 


^3L 


The  last  example,  written  in  these  clefs,  appears  thus : 


m 


t 


49 — &■ 


g 


<9 r. 


ll*^a  p  p  r^  r   -'H^ — " — f 

'^ji  1  r  1 — ^ ■ 1 

W^ 


-o- 


Exercises  in  score. 

Close  position. 
1. 


ga^ 


ist:^ 


64^6^  «^^     Ji  6  'ft 


fci:^ 


-€V 


06  6    2 

^  4 


"5.  6    '    '  e'e^e '« 


4    87 


g 


^ 


? 


zz 


3. 


66       6'6     6      i     64 
^4  8 


326    6-8  7 
4- 


Zj'\,     \'    ^     \^^ 


6  yj  f  \^^ 

6""^        ^  7 


64      ^^ 


"Of- 


4.     Open  position 


^ 


JJlirlo 


§ 


g     I  rJ 


3    «       6  •6     4 

4  3 

6.     Open  position. 


f    7 
4 


g 


ZZII 


^ 


f 


►o- 


%    ^6 


-€> 


«f    « 


6    6       It  7 
4 


CHAPTER  VII. 


85 


Cross-Relation  . 

A  very  unmusical  effect  is  often  produced  when  any  two  voices, 
one  in  one  chord,  and  the  other  in  the  next  succeeding  chord,  take 
different  tones  on  the  same  degree  of  the  scale. 


^ 


^W 


W 


i 


t 


1 


7$i^: 


■€>■ 


J 


Such  cases  as  the  foregoing  are  inadmissible  from  the  evident  an- 
tagonism of  the  voices. 

When  different  tones  on  the  same  degree  of  the  scale  occur 
in  successive  chords,  the  effect  is  always  good  if  they  occur  in  the 
same  voice,  thus: 


i 


w 


-e>- 


s 


m 


When  the  two  tones  thus  occur  in  the  same  voice,  a  cross-relation 
existing  at  the  same  time  in  another  voice  is  generally  not  objec- 
tionable , thus : 


m 


r 


^ 


^ 


^ 


t 


2302 


M 


/ 


g 


m 


g 


There  are  some  cases  in  which  both  voices  move  one  or  more 
degrees,  and  still  the  antagonism  in  the  cross-relation  is  so  slight 
as  to  be  unobjectionable.    Such  cases  are  therefore  admissible ,  thus: 


E 


«=; 


t-rr 


g 


7 


4):  r  f  i<^r  r 


\>-9- 


^ 


S: 


Cross-relation   is  not,   therefore,   invariably   prohibited.     Each 
case  must  be  judged  on  its  own  merits.     It  is  usually  admissible 


86 


PARKHURST  HARMONY. 


when  one  of  the  two  voices  takes  the  two  tones  (as  explained 
above),  and  is  least  objectionable  when  the  tones  are  of  so  short 
duration  that  the  antagonism  is  least  emphasized. 

X 


Occasionally  an  unpleasant  effect  is  traceable  to  a  cross-relation 
existing  between  two  voices  not  in  successive  chords,  but  with  one 
or  more  intervening  chords,  thus : 


i 


J 


3CZ 


AA 


^^m 


^ 


^ 


31: 


A^ 


.S3l 


m 


The  only  unpleasant  cross-relation  that  can  arise  between  any  of 
the  natural  tones  of  the  scale,  is  that  which  comes  from  using  the 
fourth  and  the  seventh  of  the  scale  (major  or  minor)  in  success- 
sive  chords: 


major 


minor. 


major.  minor, 

bad.  better.best.   bad.   better,  best.  bad. 


This  interval,  an  augmented  fourth  (also  called  Tritone,  because 
the  sum  of  three  whole  tones),  can  be  used  in  cross-relation,  except 
where  it  becomes  too  evident,  as  In  the  examples  marked  "bad"; 
that  is,  in  general,  between  the  outer  voices. 

Sigiit-Reading. 
A  student  may  have  learned  all  the  details  of  chord  formation 
and  connection,  and  at  the  end,  be  quite  unable  practically  to  make 
any  use  of  his  knowledge.  The  majority  of  Harmony  students, 
after  two  years'  study,  cannot  sit  down  at  the  piano  and  properly 
connect  half  a  dozen  simple  chords.  This  is  the  result  of  that  same 
separation  of  theory  and  practice  that  has  largely  prevailed  hitherto 
in  the  study  of  a  foreign  language,  wherein  the  pupil,  after  months 
and  even  years  of  study,  cannot  speak  the  simplest  sentences,  al- 
though he  has  become  fully  initiated  into  all  the  mysteries  of  de- 
clension, conjugation  and  syntax. 


CHAPTER  VIl. 


87 


•  Tlie  Harmony  student  will  see  the  chords  in  a  new  light  when, 
with  the  bass  given,  he  plays  the  harmonies,  according  to  the  rules 
already  familiar  to  him,  without  first  writing  them.  This  process 
gives  in  a  short  time  a  practical  fluency  which  years  of  mere  exer- 
cise-writing can  never  afford. 

We  will  call  this  process  improvising  the  harmony,  or  sight- 
reading,  being,  as  it  is,  the  first  step  in  the  art  of  true  improvisation, 
i.  e.,  with  no  bass  being  prescribed.  Exercises  of  this  sort,  begin- 
ning with  the  very  simplest,  will  from  this  point  on  be  interspersed 
with  the  usual  work  of  the  student,  and  it  is  urged  upon  the  pupil 
not  to  forego  the  advantage  to  be  derived  therefrom.  Even  if  he 
aspire  to  be  only  a  harmonist,  and  not  a  composer,  this  practical 
use  of  chords  will  be  of  incalculable  benefit. 

The  procedure  in  the  use  of  these  exercises  is  as  follows:  Play 
the  first  bass  note  and  the  three  other  tones  of  the  chord,  with  the 
octave,  third  or  fifth  in  soprano,  according  to  the  figure,  then  deter- 
mine the  letters  of  the  next  chord,  moving  the  voices  according  to 
the  rules  in  writing,  being  governed  mainly  by  the  Three  Primary 
Rules,  With  patience  and  care  the  pupil  will  at  length  be  able  to  im- 
provise with  the  same  correctness  with  which  he  would  write.  Avoid 
placing  the  soprano  above  the  staff,  as  the  effect  of  the  harmony  is 
shrill  and  disagreeable  when  it  lies  so  high.  (In  the  first  set  of 
exercises  let  each  be  played  in  three  positions  of  the  first  chord,  i.  e., 
with  octave,  then  third,  then  fifth,  in  soprano,  as  in  illustration.) 

Illustration. 


Sight-reading. 
2. 


m 


XE 


o   !<> 


xx: 


XE 


n 


13: 


<>   'o 


3. 


m 


m 


■^>- 


3X 


XE 


xx: 


XE 


XE 


XE 


-O- 


"CE 


'y4  "  I 


€>- 


XE 


XX 


-O- 


XE 


XE 


■€>- 


s 


7. 


§ 


4V.     o 


^ 


o- 


KE 


€>^ 


XE 


XI 


XE 


XE- 

10. 


0[ 

^h\ — ho^ 


p 


-o 


XE 


xr 


€V 


88  PARKHURST  HARMONY. 

(The  teacher  should  require  the  pupil  to  play  these  exercises 
at  the  lesson.  They  should  be  played  slowly  and  practiced  sufficient- 
ly to  insure  their  being  played  smoothly  and  accurately.  For  the 
present  they  are  to  be  played  in  close  position.) 

Summary. 

Close  position: — Open  position: — Boundary  line  between  the 
two: — Allowable  interval  between  adjacent  voices: — Proper  and 
improper  succession  of  perfect  and  diminished  fifths: — Definition 
of  concealed  fifths  and  octaves: — Difficulty  of  rules  in  the  matter: — 
Explanation  of  bad  effect: — Objection  to  the  explanation: — ^When 
more  and  when  less  conspicuous: — Rule  concerning  them: — Best 
method  to  avoid  them : — Two  exceptions  to  rule : — Concealed  unisons 
when  allowed : — Writing  in  score : — How  tenor  is  written : — Cross- 
relation  : — ^When  admissible. 

CHAPTER  VHI. 

SECONDARY  SEVENTH-CHORDS. 

All  the  seventh-chords  in  the  scale,  excepting  the  dominant- 
seventh,  are  called  secondary  seventh-chords.  The  reason  for  this 
will  appear  later. 


kii'"^^i 


One  of  the  commonest  uses  of  the  dominant-seventh  is  in  con- 
nection with  the  tonic  chord: 


-^ 


"^^ 


iY   " 


m 


In  this  formula  the  bass  ascends  a  fourth  or  descends  a  fifth,  and 
the  progression  of  the  other  voices  has  already  become  familar  to 
the  pupil.  On  account  of  this  familiarity,  the  secondary  seventh- 
chords  are  at  first  made  to  progress  similarly,  although  it  will  be 
found  in  a  subsequent  chapter  that  we  are  by  no  means  confined  to 
this  progression.    The  tendency  of  the  seventh  in  all  seventh-chords 


CHAPTER  VIII. 


89 


is  invariably  downzvard,  even  though  the  seventh  of  the  chord  be 
the  leading-tone  of  the  scale  : 


4  "  »  ^ 

In  the  dominant-seventh  chord,  the  third  is  the  leading-tone,  and 
has  a  natural  upward  leading : 


I 


o       <> 


^=^ 


^ 


but  in  the  secondary  seventh  chords,  the  third  has  no  such  quality, 
and  has  greater  freedom  in  its  progression : 


I  fulua 


^ 


^ 


XE 


^ 


XE 


The  foregoing  formula  for  the  resolution  of  the  seventh  chord 
(i.  e.,  in  which  the  bass  ascends  a  fourth  or  descends  a  fifth,  and  the 
other  voices  progress  accordingly)  is  common  in  all  the  secondary 
seventh-chords  except  two,  viz.,  that  on  the  fourth  of  the  scale, 


I 


^ 


s 


-o- 


5=SF 


g 


M^-^ 


-ii. 


-^ 


where  the  progression  of  the  bass  is  objectionable,  and  also  results 
in  the  unsatisfactory  common  chord  on  the  seventh  of  the  scale ^ 
and  the  one  on  the  seventh  of  the  scale. 


^ 


^^ 


XT 


m 


331 


fvhich  is  not  objectionable  like  the  preceding,  but  is  far  less  usual 


90 


PARKHURST  HARMONY. 


than  that  progression  in  which  the  bass  moves  onl\  one  degree  to 
the  tonic  ,  thus  : 

b.  c. 


i 


V   good 


bad 


^¥r 


XE 


O- 


JOL 


:n: 


-€>- 


XK 


(The  progression  at  (b)  is  bad,  because  of  parallel  fifths ;  the  effect 
at  (c)  is  good,  notwithstanding  the  concealed  octave,  which  comes 
out  so  prominently.  We  have  also  at  (c)  the  doubling  of  the  iifth, 
which  is  allowable  in  this  connection.) 

The  resolution  of  the  secondary  seventh-chords  will  not  be  diffi- 
cult after  the  foregoing  explanations,  but  attention  will  be  neces- 
sary to  feel  the  exact  effect  of  each,  they  being  different  from  each 
other,  and  from  the  dominant-seventh,  as  regards  their  constitution 
of  major  or  minor  third,  perfect  or  diminished  fifth,  major  or  minor 
seventh. 

The  Preparation  of  the  Seventh. 

A  discord  which  is  altogether  too  harsh  when  it  enters  abruptly, 
often  becomes  serviceable  when  the  ear  has  been  somewhat  prepared 
for  it,  whereby  the  harshness  is  in  a  measure  softened.  Thus  the 
discord  at  (a)  enters  abruptly,  and  is  intolerable,  but  at  (b)  the  ear 
is  prepared  somewhat  for  the  effect,  and  the  same  interval  becomes 
allowable : 

b 


I 


f  'r  I'  "  r 


^ 


f 


Illustrated  in  four-part  harmony  thus : 
not  prepared.  prepared. 


not  prepared 


i4-tj   J  1 

1  g  1  j  J  II 

H^ 1 u 

From  the  above  examples  it  is  seen  that  the  ear  is  prepared  for  the 
discordant  effect  by  hearing  that  tone  which  forms  the  discordant 
interval  in  the  preceding  chord,  and  in  the  same  voice.  The  neces- 
sity of  the  tone  being  in  the  same  voice  is  seen  in  the  last  example 
above,  where  the  identical  tone  is  heard,  first  in  the  alto,  then  in  the 


CHAF1Ek///f. 


91 


soprano,  but  the  ear  is  not  thereby  prepared.  (In  usual  phrase,  the 
tone  is  said  to  be  "prepared";  but  to  state  it  exactly,  it  is  the  ear.) 

The  effect  of  the  dominant-seventh  without  preparation  is  satis- 
factory, but  the  secondary  sevenths  in  general  being  more  harsh, 
need  preparation.  Exactly  why  this  distinction  exists  is  not  easy 
to  explain,  but  the  fact  is  evident,  and  needs  no  argument. 

We  have  then  the  following  rule : 

The  seventh,  in  secondary-seventh  chords,  must  be  prepared  by 
appearing  in  the  preceding  chord  atid  in  the  same  voice. 

The  followin£>-  illustrates  the  preparation,  in  different  voices,  of 
the  several  secondary-sevenths : 


(In  the  seventh-chord  on  the  seventh  of  the  scale  (as  in  the  last 
example)  that  position  is  far  better  in  which  the  seventh  from  the 
root  is  in  the  soprano:  (a)  is  better  than  (b)  or  (c).  Tlicre  is  less 
need  of  preparing  this  than  any  other  of  the  secondary  sevenths,  as 
the  effect  is  less  harsh. 


I 


*R= 


Illustration. 


g  ^  1^  g  i-g^ 


t^^^idfAfim 


% 


f 


t 


0    7 


92 


PARKHURST  HARMONY, 
Exercises. 


1. 


g 


zz: 


m 


I 


TH^'  ^  'f  , 


XE 


3     6       '7 


«         ?. 


r; P 


f 


T7 — n5^ 

2    6       7 


T~^ 


8. 

r  ^^     4 1 

=*Wt 

f=Ft 

'2 

Cfi 

-ts>- 

N=^ 

_ 

— 

f-fs-j-is^ 

HI 

W 

6 

7 

-4-^ 

7 

^ 

LS 

'^erg'si;  1 

L«_1J 

s 


3 


f 


7^       67 


5. 


2    6       ^ 


i 


g 


XH 


6. 


7        8    7 


Tjr 


m 


^j  r^    -i» 


f 


11^ 


T^ 


6    4 


7; 


^ 


i 


^ 


O- 


«>-" 


8. 


5       6    7 


gp=g 


i 


s 


zz=e 


^ 


n: 


ys    6 

9.    open  portion. 


6  ^     8  7 


»=<>  JLJ 


J  P    \!'   rl 


Pi 


'6        6  '6  -3)- 


6 
5 


5  7  « 

10.    open  position? 


^ 


s 


^ 


xnm 


M 


Series  of  Seventh-Chords. 
The  resolution  of  the  seventh-chord  has  heretofore  been  a  com- 
mon chord,  on  the  fourth  above,  or  fifth  below.    But  it  can  as  well 
l)e  a  seventh-chord,  which  in  turn  may  be  resolved  by  still  another 
seventh-chord ,  thus : 


M 


t^ ^ 


^ 


^sw=^ 


xx: 


4  pTjjTy 


or 


55i={^ 


1 


^    ^     77      7 


fi        7 


-iS—K 


111 


Xfl 


33: 

jce: 


CHAPTER  VIII. 


93 


No  difficulty  is  involved  in  the  substitution  of  a  seventh-chord 
for  the  common  chord,  but  it  will  be  observed  that  the  third  of  each 
sez'enth-chord  (as  above)  becomes  the  seventh  of  the  next  chord, 
and  therefore  remains  stationary ;  also  that  by  adopting  the  simplest 
progression  of  the  voices  the  fifth  is  omitted  in  each  alternate  chord; 
irom  which  we  derive  the  following  rule : 

In  a  succession  of  seventh-chords  in  the  fundamental  position 
omit  the  Afth  in  each  alternate  chord. 

Exercises. 


1. 

^\' 

n 

•l* 

-A 

y     rJ 

-^ 

r) 

-fe! 

A\-. 

2-^ 

w 

7      7 

7      7 

7      7 

7 

6    ^ 

1, 

1 u 

^^ 


F^ 


A2L 


g 


:^. 


6     6 


^^ 


^ 


'     6  6        ' 


6     7 

f2  ^ 


677 


g 


O- 


67      777777  67 


5. 

Frf=] 

P=t=i 

ff=^ 

-f-f- 

1 ^1 

3     6 

1 

6 

7  7 

j=^ 

6   * 

-Al L^ 

^ 


^7-|» 


s 


J  I.J  ^  1^^  f 

^         A  a    la 


-^^ 


^ 


7:    open  position. 


«    I 


9    '6 


i 


J    '^    1^^    rJ    If    j    1^^    j   N    J    I.J    g 


^ 


5    ¥ 
8.  open  position 


^ 


"5"  777777        77 

Secondary  Seventh-Chords  in  Minor. 

Their  use  is  more  limited,  owing  to  the  awkward  progression  in- 
volved through  the  raised  7th  (G#  in  A  minor).  Three  are  service- 
able, on  the  2nd,  3rd  and  7th  of  the  scale. 


7    ^ 
^     7 


94 


PARKHURST  HARMONY. 


2nd 


3rd 


on 


7th 


iiB:4?^f?si^:?^ti2;rti 


3XCC 


^ 


TF 


^«: 


^^ 


L^. 


ito  ^Itfito  |it^ 


^w 


33E 


XE 


XE 


3X 


n    i      1    i      1  7  7  7  7 

Those  on  the  2nd  and  3rd  require  no  special  mention ;  that  on  the 
yth  is  a  new  and  important  chord,  known  as 

The  Chord  of  the  Diminished  Seventh. 
a*^ —         _      .A 


^ 


^ 


w 


-♦>- 


-€»- 


XH 


bad. 


good. 


^ 


o: 


fe^ 


bad. 


good. 


bad. 


good. 


7       -5^         7  7  7  -7  7 

The  usual  progression  (into  the  chord  on  the  fourth  above  (G#-C) 
is  impossible,  as  the  progression  of  the  bass  is  not  allowable,  and 
the  chord  on  the  third  of  the  minor  scale  (with  an  augmented  fifth) 
is  not  satisfactory.  The  progression  of  the  bass  is  therefore  one 
degree  upward,  (as  in  the  seventh-chord  on  the  seventh  of  the 
major  scale),  and  the  third  must  not  be  allowed  to  move  in  fifths 
with  the  seventh  as  at  (a)  above. 

The  Diminished  Seventh,  the  softest  of  all  sevenths,  needs  no 
preparation.  There  are  three  sizes  of  the  seventh-interval;  major, 
minor  and  diminished, 


$ 


-o- 


^ 


and  they  are  harsh  in  proportion  to  their  size. 

Write  the  following  diminished  seventh-chords,  in  different  podf- 
tions,  also  in  close  and  open  position,  and  resolve  properly ; 


7'^  <!»  "  11^*11  it.^o  ii¥ti"°  qffit^ 


3x: 


^S 


0E 


300 


^^ 


^ 


-»- 


31: 


7  7  '7  7 

The  seventh-chords  on  the  ist,  4th  and  6th  of  the  scale  involve  pro- 
gressions which  are  either  utterly  impracticable,  or  rarely  service- 
able, thus: 


CHAPTER  VIII. 


95 


on 


ist        on  4tji 


on 


6ib 


<>8-ii"»<t8  '»  i 


it    S>c\\\\    8 


XE 


-•» — ► 


W=ff 


i 


# 


better 


£C 


XIL 


better. 


•4^ 


XE 


Illustration. 


'-&- 


-o- 


"^        7 


a 


^ 


=2 


z:sc=3 


«>^ 


«==^ 


t:^ 


4>^ 


*^ 


f 


fczi 


XE 


7 


Exercises. 


1. 


^ 


r  i  i''iiJ  1'^  1°.  if^ 


36       7^ 


2. 


7 


^ 


XE 


3. 


s 


^ 


^^ 


^^^ 


-2; — fi^ 


3       6    "T"^ 


s^^^^^^ 


6  -6^ 
4 
it 


rr-t©- 


^ 


3 


i 


6    7 


19 r 


^—-&- 


\   \    \\    ?  \^-A 

6  4-61  67 


o- 


6. 


6       7     « 


4    % 


^ 


^ 


2  JgfJ  1^  ft)  H  >.- 


«- 


3  6-6^  ^      6 

4 
3 


"y-    open  position. 


^ 


I 


5     4  i  ,  ^ 


^3 


^-    open, position. 


^S 


^  'uj  '^j  y^^ 


tT 


6    8  7 

4  i 


96 


PARKHURST  HARMONY. 


A  more  musicianly  effect  is  obtained  by  holding  over  the  tone; 
instead  of  repeating  it,  when  it  belongs  to  the  same  voice  in  two 
or  more  successive  chords.  This  is  illustrated  in  the  first  two  meas- 
ures of  the  first  of  the  above  exercises  in  open  position. 


i 


* 


^ 


^=f^=H 


3CE 


^ 


f 


jh: 


31 


^ 


bettelr. 

J2. 


i 


r 


■A-    "6 
3 


Two    EXCEPTIONS    TO    THE    RULE    THAT    SECONDARY-SEVENTHS    MUST 

BE  PREPARED. 

First  exception :  When  the  secondary-seventh  chord,  by  the  use 
■of  accidentals,  takes  the  form  of  a  dominant-seventh-chord  ;  i.  e.,  has 
a  major  third,  perfect  iifth  and  minor  seventh;  thus : 


_  bad. 


good- 


ood. 


/ 


^ 


'I  lU  Mill  II  I, 


Every  chord  that  is  altered  in  this  way  is,  in  fact,  a  dominant- 
seventh  chord  of  some  scale,  but  as  used  above  is  only  a  secondary- 
seventh  chord  altered  to  that  form,  there  being  no  actual  change  of 
scale. 

Such  a  free  entrance  of  the  seventh  as  the  above  will  however  be 
comparatively  infrequent,  as  the  simplest  harmonic  progression  will 
usually  involve  preparation,  thus: 


m 


I 


XE 


7 

i 
Second  exception:    When  one  of  the  voices  moves  diatonically 
through  the  sez'enth,  in  the  unaccented  part  of  the  measure,  thus: 


F^ 

S 

/^  ^ 

CHAPTER  Vni. 

rU 

h^T- 

97 

#= 

^ 

^ 

:s:?= 

_ 

-^ 

Nf^ 

rfti 

r4 

1 

-X- 

tf 

-^ 

1  «» 

i> 

4> 

?s| 

8    7  87  87  87  87 

(Note.  The  matter  of  accent  is  fully  explained  in  Chapter 
XVI.) 

This  use  of  the  seventh  will  be  referred  to  again  under  the  sub- 
ject of  passing  tones,  (Chap.  XV.)  and  may  be  designated  as  the 
passing  seventh.  It  is  found  frequently  in  the  inversions,  as  well 
as  in  the  fundamental  form ,  thus : 

.     isj- inv.     2pdinv.  3rd  inv. 


feF^ 


^ 


"    |o    U>— Iq-I  o 


se 


w 


Al 


n 


&-r. 


46  26-  '6-         -6- 

3  5  5  5 


TH 


6  - 
5 


4     8  7 
3 


As  the  above  example  shows,  when  the  passing  seventh  occurs  in 
the  bass,  it  results  in  a  chord  of  the  second,  and  can  be  so  figured ; 
but  it  is  usual  in  such  case  simply  to  put  a  dash  ( — )  under  the 
seventh,  which  always  means  that  the  other  voices  are  to  continue 
the  harmony  of  the  previous  chord.  This  does  not  mean  that  the 
other  voices  must  remain  immovable,  but  if  they  move,  it  must  be 
to  tones  of  the  same  harmony,  thus: 


^\;}hVm^\^^.m 


-o^ 


9,   l<^0|fe-7: 


^^ 


^y 


33: 


'^ 


§ 


I 


s 


^^m 


3X 


O 


6'-       6        if-       6         9-6?-6 
5  5  5 

Write  the  following  fragments,  changing  the  position  of  the  har 
mony  in  the  second  chord  of  each : 

close  position.  open  position. 


m 

-z^ 


^Try 


% 


i'^l\J\m^\ 


2:^ 


TSL 


8-6 


-     6 


6  8-6 

The  harmony  in  such  cases  is  to  be  changed  chiefly  for  the  sake 
of  securing  a  better  location  of  the  voices,  or  to  avoid  monotony. 


98 


PARKHURST  HARMONY. 


The  pupil  must  use  his  own  judgment  as  to  whether  the  voices 
should  move,  or  sustain  the  tones  of  the  previous  chord.  Paral- 
lel motion  of  all  voices  is  here  allowable,  as  on  page  56. 

Illustration. 


^^^fc^3#ato 


r  prrM'f 


r^ff r  "^ 


3-66       7     56'78-77'-6 


XE 


20? 


7    7 
Exercises. 


2f— -TV 


1. 


^ 


41:  » r^ 


^ 


.3.  8«        43        e "^  ^ 


-T^ff 


\\p  \ii<> — 1-^ 


^ 


SP 


^ 


zang: 


tl7 


^5» ^iT^ 

6 


6      6 


T~6" 


3 .    ope n  position 


m 


a 


^ 


■«=»- 


^ 


3X 


6      8  7 


-? 


67 

4 


6     7  8-7 


4.  open  position 


V     I  P  \?rJ 


m 


fS   fJ      -^ 


6  ^^ 

8  7 


&-HV 


Tir 


S 


5ii 


5.   close  position, 


^^ 


xn 


22 


k!6  6      67 


6. 


^^T^.n 


^\ 


s 


^V 


H 


tf-K»- 


7, 


5     87        6     8  7    '     6      8  '^ 


^ 


*f   P  /v 


<^ 


.  4- 


^ 


l«      W 


^»-7: 


30: 


*>         35e  6  '7  87  '**" 


iJ  6   4 

8.  ,  in  sco^e.3 


W-|^      6 


"'I,  iijr  iii,i^ijiiii,iii,ijij  II 

5  !<         ^-f  -      <>      0  -(.     ,i57 


CHAPTER  VIII. 


90 


Sight-Reading. 

Primary  and  secondary  common  chords. 
^   MajoViicale. 


i 


1 


'^  Ir  Jlf  J 1^^  ^ 


r: — (^ 


30E 


J     rJ     zzz=z:rz:±z  I      ±11:  =  : — ?:>— :zzzrii-p— izuzcr 


3. 


S 


Hi[  rii  ^^  iN^i^ir  ir  ^  i^^r 


-0-" 


^M 


^ 


■*♦- 


f-^  i^j  ,j  ^pj 


m 


5.  see  page  29. 


I  II  Ml,  lull 


"^ 


-^>- 


^ 


^ 


P^^^ 


7.Minorscalc.8. 


^ 


^ 


to. 


1 


? 


fe!^ 


m 


2t^ 


tTjt ^ 


11, 


3— -ho  f- 


12.  see  page  42 


g;         fg 


r  II   I  If  (: 


XE 


18. 


14. 


^ 


5K 


i 


M(;fir(aMirf;irjiMiJii.^^ 


5'      ? 


15. 


i 


^ 


/•s -f9- 


^ 


«v 


<9^'-T&Q- 


z^r^^^--E. 


zz^xazz 


^  'Y     '^^ 


r      T 


3     r 

Chords  and  their  connections  are  not  mastered  till  they  can  be 
fluently  improvised  in  the  above  manner.  Effort  in  this  direction 
will  be  found  to  repay  far  better  than  the  mere  writing.  The 
minor  scale  presents  peculiar  difficulties,  and  a  review  of  Chapter 
III  is  advisable. 

Summary. 

Secondary-seventh-chords: — The  usual  progression  of  seventh- 
chord  on  7th  degree  of  scale : — How  the  discord  of  the  seventh  is 


100 


PARKHURST  HARMONY. 


"prepared": — Need  of  preparation  in  secondary-seventh  chords: — 
Procedure  in  a  series  of  seventh-chords : — Use  of  secondary-seventh 
chords  in  minor  scale : — Peculiarity  of  seventh-chord  on  7th  degree 
of  minor  scale : — How  it  differs  from  others  in  regard  to  progres- 
sion and  preparation  : — Three  sizes  of  the  seventh-interval,  and  their 
degrees  of  harshness: — First  exception  to  the  rule  of  preparing 
secondary  sevenths: — What  is  the  "dominant-seventh  form:" — 
Second  exception  to  the  rule  of  preparation: — Meaning  of  a  dash 
under  bass  note: — Changing  position  of  upper  voices,  and  parallel 
motion  in  all  voices,  when  "passing  seventh"  occurs  in  bass. 


CHAPTER  IX. 
The  Inversions  of  the  Secondary-Seventh  Chords. 

These  inversions  are  formed  in  precisely  the  same  way  as  those 
of  the  dominant-seventh,  and  need  no  special  explanation,  as  the 
several  elements  have  the  same  progressions  as  in  the  fundamental 
position. 

In  the  seventh-chord  on  the  seventh  of  the  scale,  both  major  and 
minor,  in  which  the  root  has  a  progression  of  one  degree  upward 
(to  the  Tonic),  care  must  be  taken  to  avoid  parallel  fifths  in  the 
first  and  second  inversions,  just  as  in  the  fundamental  position. 


Major  scale. 


^S 


^m 


SfcS  =  3^ 


baJ.      good. 


good.         bad. 


good 


good. 


bad. 


^m 


(9 — n 


^ 


^=7g 


IB — fe 


ts*— " 


5 


^ rp — --5 fjr 


Minor  scale 


i  HH  j> 


iP 


=i^=^ 


bad. 


good. 


bad.  good.  bad 

m 


good. 

J  J    IJ  J 


m 


A-    « 

'4 


5 


5 


CHAPTER  IX. 


101. 


The  third  inversion  of  eax:h  of  these  chords 
Major  scale.  .  Minor  scale 


^ 


« 


±: 


^^ 


i 


"TT 


-2 5" 

4 


4 


4 


can  seldom  be  used  with  the  resolution  into  the  ^  chord,  and  it  is 
to  be  observed  in  general,  regarding  inversions  of  the  secondary- 
seventh  chords,  that  they  are  not  as  uniformly  effective  as  those  of 
the  dominant-seventh  chord,  and  the  position  of  the  three  upper 
voices  needs  to  be  chosen  more  carefully.  In  reality,  a  large  propor- 
tion of  all  secondary-seventh  chords,  fundamental  and  in  inversion, 
that  are  practically  used,  are  altered  into  the  "dominant-seventh 
form/' 

Illustration. 


i  i'hih^k\l^p^^\l^^h'}'^ 


=yF^ 


t  s 


J* II  .ji  lyju.JiJi 


» ,  •••  I " 


Exercises. 


m 


m 


i 


1 


3     16      't 


t 


m 


WW 


T-T 


i5~^ — nrr 

5 


m 


t 


^  \rj 


6     '  6  6  7  '  Q  ^ 


I  If  i  i-i  ;'  If 


3: # 


77-1^ 


^^ 


i 


S 


ZI3I2Z 


&=IZZ 


^ 


^izi 


xn 


6 


^T"^ 


5. 


t^      o 


*):,   a  o   5- 

if 

^ 

,r;   p 

— 

— H 

y  >  g       1 — 

6 

1 

jLl_y3 

o  ^  — 

if 

— w 

3     6 

3 

\-'— 

T^ 

6    ^ 

1 (5l — 1 

^3^ 

'-or" 

102 


PARKHURST  HARMONY, 


». 


^s 


^g*  i^jg* 


^ 


^6  6    'U 
5  ^3 


g 


i 


S 


^ 


^ 


F5 


r^ 


xx 


tS'-sHS^ 


3#    ^ 
8.  open  position. 


-^ 


7   mr. 


^@ 


*>^ 


m 


XE 


IT 

«5 


<^-U 


8  7    8  7 


^'     open  position. 


6     '6  '6      6 
4       5 


^T 


*mHJI"JN 


7    I^?         6  4  7 
i^         6         4  3  I 


in 


10. 


ii     567 


-6      7  7  7 


7 


'^'■"l![iriff;l|fJJIyjJjJllAlllUl   II 

5    4  er^     5  4 


i 


Sight-Reading. 

With  first  inversion  of  common  chord. 


^ 


i 


xr 


TIMS' 


2^    « 


§ 


zz 


Xfl 


-z; ^ 

6 


^ 


m 


f 


zz: 


^ 


2Z 


3 


itV  ■       (9 


§ 


t 


^3 


"cr 


5. 


g 


^ 


3Cf: 


%     t 


6    T 


Let  the  basses  of  the  following  exercise  be  correctly  figured,  so 
as  to  express  all  that  is  involved  in  the  harmony  of  each  chord. 
This  is  just  the  reverse  of  all  the  foregoing  exercises,  in  which  the 
figured  bass  is  given,  from  which  the  harmony  is  to  be  determined. 


CHAPTER  IX. 

-A. 


103 


K^'f  ^'fiiiJ  jj^iff|iiiijj  I 


J  I .  If  riif  If^ 


3 


^^ 


^^m 


^ 


1^ 


^  *#*^  •  • 


g 


^ 


g 


^ 


^ 


j^|MHljJ■■ilil■^li.^iJlJ^Jll 


m 


^ 


P^ 


15^— U 


4jl^^,ij  i/"V-^  I  iri  j  i  i^j-^^ii  jJ 


i 


p^ 


* 


aac 


f 


^^P^^^^^ 


^^ 


2EP 


^ 


P 


^^"'^1-     jljj^r'i 


P 


r  r  '-^f^i'-^ 


S 


*t 


f 


? 


^  r  ij  ^r 


Mi:± 


It  would  be  well  for  the  teacher  to  write  additional  exercises  like 
the  foregoing,  to  be  figured  by  the  pupil. 

Summary. 
Formation  and  progression  of  inversions  of  secondary-seventh 
chords : — Caution  in  progression  from  seventh  chord  on  7th  degree 


104 


PARKHURST  HARMONY, 


of  major  or  minor  scale,  in  fundamental  or  inverted  form: — Inef- 
fectiveness of  most  secondary-seventh  chord  inversions,  and  need  of 
care  in  position  of  upper  voices : — Frequency  of  ''dominant-seventh 
form''  in  secondary-seventh  chords. 

CHAPTER  X. 
Seventh-Chords  Followed  by  Various  Resolving  Chords. 

The  essential  thing  in  the  progression  from  a  seventh-chord  is 
that  the  seventh  descend  one  degree.  The  resolving  chord  hereto- 
fore used  has  always  been  the  common  chord  (or  seventh-chord), 
founded  on  the  fourth  degree  above,  or  the  fifth  degree  below  the 
root  of  the  seventh-chord  to  be  resolved ,  thus : 


iUi^-l 


53 


m 


w^ 


m 


rz. 


The  one  exception  thus  far  has  been  the  seventh-chord  on  the 
seventh  of  the  scale,  major  and  minor,  the  root  of  which  moved  one 
degree  upward. 


But  any  chord,  having  a  close  harmonic  connection,  and  allowing 
of  the  proper  resolution  of  the  seventh,  may  also  be  used,  what- 
ever the  root-progressions. 

The  various  chords  that  can  follow  the  seventh-chord  may  be 
divided  into  two  classes : 

1st,  those  in  which  the  bass  moves: 

2nd,  those  in  which  the  bass  is  stationary. 


CHAPTER  X. 


105 


First  Class. 
(a)     Bass  moving  one  degree:  (major  or  minor  second). 


^M^ 


53^ 


mEimsm 


^w 


J. 


i 


i^ 


m 


§ 


^z^-.is:^ 


^rs 


m. 


5.6^3  435 

5 


It  often  happens  that  a  progression  that  is  inadmissible  in  one 
position  of  the  upper  voices  is  allowable  in  another  position ,  thus : 


bad. 


good. 


i 


(b)     Bass  ascending  an  augmented  Prime. 

m 


i 


^0 


m 


VI — ^- 
Second  Class. 


Bass  stationary. 

With  stationary  bass,  the  resolving  chord  can  take  the  form  of 
any  one  of  the  five  chord-inversions,  viz.,  6,  J,  e^  4^  2,  thus : 


i 


m 


E 


TTO 


Til r. 


3X 


"tM 


«^ 


:gr 


•^^^ 


^ 


>^-7:^ 


^ 


-«^    ^ 


XE 


fc33: 


:ii: 


33: 


3x: 


IE 


o* 

7    6 


1    A      ^ 
0 


4  2 


5 


With  stationary  bass,  the  seventh-chord,  ivlicn  itself  an  inversion, 
most  naturally  resolves  into  a  higher  inversion  of  another  seventh- 
chord  , thus : 


06 


PARKHURST  HARMONY. 


4  'J  :J°  I J 


;^ 


3 


^ 


_«JL 


fetJ 


S 


^Y    o 


5         3 


"6 — sr 

5 


-6- 
4 
3 


The  form  of  resolution  used  in  the  preceding  chapter  may  be 
called  the  fundamental,  as  it  is  certainly  the  more  conventional  reso- 
lution. The  several  resolutions  offered  in  the  present  chapter  afford 
a  great  and  pleasing  variety  in  the  harmonic  coloring ;  but  the  par- 
ticular  situation  must  determine  the  fitness  of  each  and  all  of  them. 
As  the  harmonies  become  richer,  and  the  chord-connections  more  in- 
tricate, it  will  not  be  amiss  again  to  remind  the  pupil  that  his  success 
depends  more  and  more  upon  his  having  a  clear  sense  of  each  har- 
mony, and  of  its  flow  into  the  following.  If  any  example  or  exer- 
cise cannot  be  thus  heard  in  the  mind,  it  should  be  played  over,  until 
the  pupil,  without  playing,  can  recall  the  whole  effect. 

Illustration. 


23C3=  23=33 


jMm^ 


jijpfi^rf  ifl 


SXi 


«i^ 


i 


■^ — r 


i 


^$ 


'HS^-i©- 


A 


TXH 


3V     'ea'e'ie     e'?'^  ^  '     « 'h  "2  'e  l^,  "   g^ 


Exercises. 


^ 


^ 


^ 'J    lis 


ZZ 


y 


^^^^^^ 


i 


JJ  '6  '6     '4  6  y    '6 


_ffl- 


7^ 


t 
3 


6687 
5 


S 


9^W^ 


3-66         7     « 


^^ 


:oi4 


3.^  .    ^A 


^      ;        8  7 


2=-P— S^ 


JV    6       f^«      *~ 


cr 


5      T 


^^ 


ft       2    6       "i    «      -|    6 


m 


f  J,  I  .v^-f  hJ^-n'^^  ^4f-j 


-*»- 


CHAPTER  X. 


107 


5. 


^^ 


i 


^3=1 


IZ. 


m 


.5     6        7  ^ 
6-  3 


t   "^ 


2 L 


i^ 


-cv 


^ 


^ — 

8  7 


6    8  7 
5 


-«>- 


p  sp 


<^    g> 


t     7 


^ 


6         6^ 

S.  open  position. 


1 


XII  33E 


-€> 


-O 


«V 


rj2 


zzig 


XX 


^S^:3ci 


t^f 


5  8^r2  6      3  :?"  ^ 


66 
4 


6467 
53 


87 


SiGTTT-RE  NDING. 

With  second  inversion  of  common  chord. 


? 


1. 


ra: 


xr 


FT <^ 


^ 


-S^ 


3a: 


z. 


3.   3      ' 


I 


O- 


irrr 

4  3 


4   3 


s 


'5    '6    ^    '  6  5     ♦^    ^      'T^^^g^   &^    ^    6        *^ 


^ 


6  5 
4  3 


i 


i^i^ 


XE 


^ 


XE 


6    5      6 
4    3 


^ — '^ 


6     5 
4     3 


5. 


3 


i^ 


XE 


4 


"cr 


^" — — yr  '  »  _>    '  *  u 


xr 


17 


4  jr 


r^ 


It  is  a  very  interesting  and  profitable  exercise  for  one  pupil  to 
play  an  exercise  slowly,  and  another,  by  listening,  to  determine  and 
name  the  successive  chords ;  indicating  them  either  by  the  letter  of 
the  root,  or  its  degree  in  the  scale.  When  it  is  impracticable  for  two 
pupils  to  practice  this  together,  the  teacher  should  make  it  a  part 
of  the  lesson-exercise. 


108 


PARKHURST  HARMONY. 


The  very  simplest  exercises  (involving  only  the  primary  common 
chords)  should  be  first  used  in  this  way,  and  other  chords  added  by 
degrees. 

Summary. 

The  essential  thing  in  progression  from  a  seventh-chord :— The 
resolving  chord  heretofore  used,  with  one  exception: — What  other 
chords  can  be  used  to  follow  a  seventh : — How  classified. 


CHAPTER  XL 
Exceptional  Modifications  in  the  Resolution  of  the  Seventh. 

While  the  fact  remains  that  the  seventh  demands  the  degree 
below  for  its  resolving  tone,  it  is  possible,  without  doing  violence 
to  this  inherent  quality  and  demand  of  the  seventh,  to  introduce 
some  modifications  in  the  chord-progressions,  which  prevent  the 
monotony  of  invariable  uniformity. 

These  modifications  may  be  classified  thus: 

1st.     Delaying  the  resolution. 

2nd.  Moving  up  from  the  seventh  and  resolving  in  an  under 
-voice. 

Each  of  these  modifications  will  be  variously  illustrated.  The 
pupil  should  carefully  study  the  examples  of  the  second  class  es- 
pecially, as  it  is  generally  impossible  in  a  figured  bass  to  compel  the 
unusual  progression ;  in  most  cases  it  being  possible  so  to  har- 
monize as  to  avoid  it  entirely. 

1st.     Delaying  the  resolution. 

This  can  be  done  in  two  ways : 

First,  by  moving  the  voices  from  one  position  of  a  seventh-chord 
to  another  position  of  the  same  chord,  or  by  the  use  of  successive 
inversions  of  the  same  chord,  thus: 


J  i  ^.  h  ^  J 


XE 


& 


^=^ 


11 


^ 


3X 


XIJ 


The  mark  x  shows  the  transference  of  the  seventh  from  one  voice 
to  another.  Naturally  the  resolution  follows  in  the  voice  that  last 
contained  the  seventh. 

Secondly,  by  so  moving  the  other  voices  that  the  original  seventh 
appears  as  another  interval  in  one  or  more  chords  before  the  reso- 


CHAPTER  XL 


10^ 


lution.  The  resolution  may  appear  in  the  same  voice  as  the  original 
seventh,  or,  if  the  tone  that  is  the  original  seventh  be  transposed^ 
the  resolution  may  also  be ,  thus : 


i 


XE 


i 


^ 


■^ 


■€*■ 


^ 


^ 


r=Tt 


f^4f^ 


M 


3nE 


3X 


5 


«: 


i 


-<=^ 


i 


XE 


6    «  "    I  ?  '  •  §     ^  T    FT 

A  +  indicates  the  original  seventh;  a  *  indicates  the  resolving 
tone.  Another  way  of  delaying  the  resolution  will  be  explained 
under  Suspension. 

2nd.  Moving  up  from  the  seventh,  and  bringing  the  resolution 
into  the  bass. 

The  bass  itself  can  ascend  or  descend  to  the  resolving  tone,  ia 
the  two  following  ways : 

fj:^.  b. 


"Z 


-^ 


6        3      6,      -'        <5 

Resolving  into  unison,  as  at  (a),  is  admissible,  but  is  more  harsh 
than  resolving  into  octave,  as  at  (1)). 

This  substitutionary  resolution  in  another  voice  can  occur  only 
in  the  bass,  because  that  voice  is  so  prominent  as  to  give  the  resolu- 
tion with  nearly  the  same  force.  The  following,  with  the  resolution 
substituted  in  the  alto  or  tenor,  are  not  satisfactory. 


^^ 


» 

^ 


pen 


^ 


33: 


* 


XE 


110 


PARKHURST  HARMONY. 


An  imperfect  fifth  can  follow  a  perfect  fifth,  but  not  vice  versa; 
accordingly  the  progression  at  (a)   is  inadmissible,  but  correct  at 

(b). 


^ 


b.-f 


good.   good   bad. 


s: 


bad 


f 


JQl 


p 


bad 


good. 


m 


f 


JOE 


T 


In  regard  to  the  case  at  (b)  it  should  be  observed  that  the  sub- 
stitutionary resolution  in  the  bass  is  seldom  satisfactory  when  the 
seventh  has  occurred  in  the  soprano,  but  is  quite  adequate  when  it 
is  in  alto  or  tenor.  The  reason  is,  that  the  seventh  is  most  conspic- 
uous in  the  soprano,  and  the  resolution  must  be  equally  emphatic 
by  occurring  in  the  same  voice. 

A  voice  giving  the  seventh  of  the  chord  may,  before  resolution, 
pass  to  another  tone  of  the  same  harmony,  and  sooner  or  later  the 
seventh  be  resolved  in  the  same  voice,  or  in  another  voice,  thus: 


$ 


^. 


^— xg 


-^ 


IDL 


XE 


XH 


XE 


-€♦- 


xs: 


XE 


XC 


-^ 


jfy 


-^ 


5  5  S        ^    i 

The  greatest  deviation  from  the  simple  and  normal  resolution 
of  the  seventh  is  that  in  which  the  voice  containing  the  seventh 
moves,  together  with  other  of  the  voices,  to  an  entirely  different 
harmony ;  while  the  resolution  occurs  later,  either  in  the  same  voice, 
or  in  another  one  ,  thus : 


^Jr-JUJj^ 


^^^^^ImpMS^f^^ 


— '74      K  kfl    «  '4 


i 


:?2: 


^-yr 


(>      -4^ 


5    4     5    3  •>      *  i!5 

All  the  essential  deviations  from  the  strict  and  immediate  reso- 
lution of  the  seventh  are  exhibited  in  the  foregoing  examples,  which 


CHAPTER  XL 


111 


should  be  carefully  studied  that  they  may  be  understood  in  the  har- 
monic analysis  of  music,  and  that  the  pupil  may  himself  introduce 
them  as  occasion  offers.  Such  treatment  of  the  seventh  will  ever 
remain  exceptional,  and  finds  its  justification  chiefly  in  the  more 
melodic  character  of  the  voice  containing  the  seventh,  and  in  the  de- 
mand for  variety  of  effect.  The  following  exercises  afford  fre- 
quent opportunity  for  this  treatment  of  the  seventh.  Let  the  pupil 
avail  himself  of  each  opportunity,  that  he  may  gain  practical  fa- 
miliarity with  the  subject. 

Illustration. 


^ — -^    >5 — 6      7 
4 
3 

Exercises. 


Ii7 


i. 


m 


mn^ 


SH 


3: 


-^ 


z±±^ 


2.'  ^'       I  '''     I 


H^ 


m 


i  '^  iC  ^M  ^i  ig^^J »' 


rt 


3. 


§ 


»i;.  '6  j9 


J  r  P  r^  J  J  J  * » 


n: 


:fcfc= 


4  3 


Z    4 
3 


7^^ 


§ 


^35 


;;^fep 


I 


i 


■€>= 


5^ 


«=Z^ 


''^  hi  4        4  4  8  7 


^61,7 
4 
5.     open  position. 


^1  « 


^ 


§ 


^ 


S 


XH 


33: 


^-^ — h«        6   b       4      ^         7    6      fcl6 ^68 

4        4   3       I     j?        !,5  4  4 


3 

6.    open  position 


S 


td  '4  6 
35 

7.  open  position. 


^^^^tFtR  fi  r/  Lr 


:/^it  6  ^i  \? 

• ^ 37 — tr: 


i 


^B^ fF 

4 
3 


4 


B    7      '6  14- 
5  4    2 


O — 
'6     8  7 

5    i 


112 


PARKHURST  HARMONY. 


The  foregoing  is  perhaps  the  hardest  set  of  exercises  thus  far/ 
and  requires  careful  attention  to  introduce  effectively  the  unusual 
progression  of  the  seventh. 

Sight-reading. 
With  common  chords  and  their  inversions,  major  and  minor. 
1. 


^ 


xn 


f 


^ 


ICE 


43 


-3^-^ 


656 
43 


6  6 


§ 


^ 


^ 


XE 


^ 


--^'W'" 


IT 


m 


n 


m 


-o- 


T^ 


4. 


2Z 


^^^ 


«    6 


6 


IT 


Summary. 


Two  ways  of  modifying  the  progression  from  a  seventh-chord: 
— Two  ways  of  delaying  the  resolution: — In  which  voice  only  the 
substituted  resolution  can  occur,  and  why : — Why  bass  is  inadequate 
as  substitute  for  resolution  of  a  seventh  in  soprano: — This  excep- 
tional resolution  of  the  seventh  is  justified  by  what  ? 


CHAPTER  XII. 

Altered  Chords. 

One  or  more  notes  of  our  two  elementary  chords  (the  common 
chord,  and  the  seventh-chord)  may  be  affected  by  accidentals.  In 
many  instances,  such  an  alteration  will  result  only  in  a  different 
variety  of  the  same  chord,  such  as  we  are  already  familiar  with,  as 
changing  a  major  chord  into  a  minor,  or  vice  versa. 


I 


=^m 


fe 


m 


In  other  cases,  the  accidental  converts  the  chord  into  some- 
thing radically  different,  so  that  the  notation  is  faulty  as  expressing 
the  intended  effect ;  thus 


CHAPTER  XIL 


113 


when  used  to  express 


i 


M 


UL 


$ 


♦>■ 


ff 


is  incorrect. 

In  still  other  cases,  the  accidentals  so  distort  the  chord  as  to  dis- 
qualify it  for  a  fundamental  harmony;  thus: 


I 


* 


wm 


After  eliminating  all  the  alterations  of  fundamental  harmonies, 
as  above  described,  there  remain  five  accidentally  altered  forms 
of  chords  which  are  characteristic  and  serviceable,  the  dis- 
cussion of  which  will  complete  our  treatment  of  fundamental  har- 
monies. 

Of  the  three  ways  above  mentioned  of  altering  chords  by  acci- 
dentals, the  first  re-forms  the  chords,  the  second  de-forms  them,  and 
the  third,  now  to  be  spoken  of  more  fully,  trans-forms  them. 

1st.      The  Augmented  Triad. 


|tf^l<^Hl^§ 


We  are  already  familiar  with  this  chord,  as  the  triad  on  the 
third  of  the  minor  scale ;  but  it  is  more  common  and  serviceable  in 
the  major  scale,  on  the  first,  fourth  and  fifth  of  the  scale,  as  above. 
The  augmented  interval  is  commonly  introduced  as  a  "passing 
note" ,  thus : 

1.  3.    r         I  3 


i 


m 


m 


s 


s 


XE 


-^ 


XT 


XE 


isr. 


3a: 


In  all  minor  triads,  the  effect  of  the  augmented  fifth  will  be 
found  to  be  like  that  of  a  minor  sixth,  hence  not  characteristic ,  thus : 


I 


^ 


means, 


]\4 


PARKHURST  HARMONY, 


It  is  the  fact  of  the  augmented  being  usually  preceded,  as  above^ 
by  the  perfect  fifth  (with  the  elimination  of  what  would  be  the 
"leading  tone''  of  a  minor  scale)  that  makes  this  chord  commonly 
used  in  the  major  rather  than  in  the  minor  scale. 

This  chord  can  also  be  used  in  the  two  inversions,  of  which  the 
first  is  the  better : 


1. 


2. 


^m 


o — XEzzgng:^ 


XL 


3. 


IS 


11  Hgji^, 


9: 


8  h5i 


-^^<^"-» 


O  II  11  ZJOOi 


0||0 


4> 


m 


]£ 


^m 


«€>- 


3tt: 


it  4   -  j*      5      4  -  il 


4 


By  the  addition  of  the  seventh  to  these  three  augmented  triads  we 
obtain  the  following : 


hi  \^^\\f  I'lp  T  ")  *^ 


s 


^ 


XE 


-O- 


xx: 


"T" 


<^5 


j»5 


The  first  and  second,  which  are  secondary-seventh  chords,  are 
not  effective  in  the  inversions ;  but  the  third  (the  dominant-seventh 
with  augmented  fifth)  is  good  in  all  the  inversions,  but  best  of  all 
in  the  first  and  third. 


'$Ji  l^i  llLj 


^^ 


f^=^ 


S*: 


a. 


Wl 


Xfl 


5 — n- 
3      - 


22 


Care  must  always  be  taken  that  the  augmented  fifth  and  the 
sez'enth  shall  resolve  into  octave,  as  at  (a),  and  not  into  unison,  as 
at  (b). 


CHAPTER  XII. 
Exercises. 


115 


xt 


^^ 


(9 P- 


i 


xx: 


^ 


3X 


5  -&-  — ^ 
4 
3 


B rt  5        6  « 

4  3  5 


4     7 


^^ 


xx: 


-€♦- 


xr 


-€^ 


3DC 


-€V 


xmz 


H'Er5-&-3|t5-5r6::7     66       -. 
.3.  *  4       ' 


-€♦- 


-^ 


Ijd       I   ^- 


cz: 


3tE: 


-€>- 


-^-5^ 


6 — ■    6    5  ■   7   6   "  '^     6 — ■  B    7" 
4    3     ^5  4 


S 


-^      ♦*     3  J  5  ^ 


H»- 


v'k''  j  iJitJ  it 


s 


^5= 


zz 


<3- 


^      \  tl 


'tt  H7 
5 


S 


4      -        B  6 

3     -  5  5 

r>.  open  position.  ** 


^^P 


i^zizzzj^ 


;.    fj 


a 


^  ^    iff 


^1 


■f4 
.3 


li5 


5  4 


Si(>H  r-K'i:ADIXG. 

Jf^/Z/i  dominant-scrcnth  chord. 
1. 


':^:    J     I  ('    fJ     I^S 


22—-:^ 


e*^ 


^ 


2. 


F^ 


^ 


^ 


3X 


^ 17"^ ' — ^-15 B5  7       '     I — e^B-Vl5=± 

_        4  3  ^  4  ^ 


3. 

H^ 

— ^— 

fri 

3 

r-^ 

4- 

F^^ 

^-^ 

7 

^     f> 

— ^^_5_^ 

«■  7 

--1 

Write  the  three  augmented  triads  in  the  keys  of  G,  D,  A,  F,  Bb 
a.rJ  Eb. 

Write  the  dominant-seventh  chord  with  augmented  fifth  in  the 
same  keys. 

Write  the  three  inversions  of  the  above  seventh-chords. 


rnd.     The  Chord  of  the  Augmented  Sixth. 


i 


w^ 


!I6 


PARKHURST  HARMONY, 


By  taking  any  minor  triad  with  a  perfect  fifth,  and  raising  the 
root  a  semitone,  we  obtain  a  combination  which  is  ineffective  in  the 
fundamental  position,  but  of  great  use  in  the  first  inversion,  which  is 
called  the  chord  of  the  augmented  sixth  (as  illustrated  above). 

Not  every  sharped  sixth  is  an  augmented  sixth.  A  sharped 
minor  sixth  becomes  a  major  sixth, 


I 


xr 


» 


XE 


» 


-€¥- 


€^ 


EEtM 


to: 


S==iS 


fe 


but  a  sharped  major  sixth  becomes  an  augmented  sixth.  Every 
minor  triad,  in  the  first  inversion,  affords  a  major  sixth,  there- 
fore by  raising  the  root  of  any  minor  triad  we  get,  in  the  first 
inversion,  an  augmented  sixth.  This  is  the  result  of  "inversion," 
which  is  fully  explained  in  the  Appendix  (G). 


'"''■«^ 


s 


a 


lO. 


«^ 


a  in  G. 
ff       Iff 


^ 


XE 


S 


6 

The  inevitable  progression  of  every  augmented  sixth  is  upward 
a  minor  second  (i.  e.,  a  semitone).  This  is  as  invariable  as  the  reso- 
lution of  a  seventh  downward  one  degree.  Yet  in  absolute  dis- 
tance an  augmented  sixth  is  the  same  as  a  minor  seventh.  This 
variable  requirement  of  the  same  interval  under  dift'erent  circum- 
stances is  treated  of  more  at  length  in  the  Appendix  (H). 

All  of  the  minor  triads  can  be  thus  treated,  but  only  those  with 
a  perfect  fifth  afford  a  perfectly  satisfactory  combination,  like  the 
above.    With  a  diminished  fifth,  the  effect  is  not  good. 


^^^ 


A  peculiarity  of  the  chord  of  the  augmented  sixth  is,  that  only 
the  third  from  the  bass  (the  fifth  from  the  root)  can  be  doubled,  as 
it  is  the  only  one  having  a  double  progression;  thus, 


t 


sfe 


^ 


<v 


^ 


±3p^ 


*1? 


^ 


^ 


_d_ 


^ 


XE 


jo: 


AY 


-5r 


CHAPTER  XII. 


117 


In  the  use  of  this  chord  the  precaution  must  therefore  always 
be  taken  of  doubling  the  third  from  the  bass,  either  in  octave  or  in 
unison. 

Illustr.^tion. 


Exercises. 


m. 


i 


XE 


3s: 


3    2       6 


6  -Hr 


-(t- 


H     8  7 
5 


^ 


W^ 


-€V 


-e»- 


^■irr 


1 


r 


^ 


«^-^«^ 


2"^^ 


-€♦- 


4. 


6  j6^ 


6      H 
5 


s 


22: 


f 


^ 


5-5-  -6- 

o.   openposition. 


«^1' 


B     8  7 
5    H 


^ 


3i: 


^ 


t 


#?-±^ 


3 


^' 


6-^  ~1 


-€^ 


b   b     2     B 


3rcl.    The  Chord  of  the  Augmented  Sixth-and-Fifth. 

If  to  any  minor  triad  with  perfect  fifth  and  the  root  raised  a 
semitone  we  add  the  seventh,  we  obtain,  with  its  inversions,  four 
forms  of  a  characteristic  chord,  of  which  only  one,  the  first  inver- 
sion, is  used  to  any  extent ;  but  this  one,  the  chord  of  the  augmented 
sixth-and-Hfth,  is  very  effective. 


^  Tf  5  3 


l^^^'^.JM 


m 


5 


5 


118 


PARKHURST  HARMONY, 


The  resolution  of  this  discord  offers  a  peculiar  proOlem.  The 
tendency  of  the  third  (the  bass)  as  well  as  of  the  seventh.  Is  down- 
ward, which  results  in  parallel  fifths. 


^ 


gga 


-^ 


^ 


33: 


m 


The  reason  of  the  downward  tendency  of  the  third  (i.  €.,  the 
bass)  is  in  the  fact  that  the  next  chord  naturally  contains  a  major 
third  (in  the  example,  G#),  and  the  progression  of  the  bass  (from 
F  to  G# )  is  an  augmented  second,  which  is  prohibited ;  the  bass  is 
therefore  forced  downward.  There  are  two  ways  of  avoiding  the 
parallel  fifths;  first,  by  having  these  two  voices  move  successively  to 
their  next  tones  ,  thus : 


[|lirl»"V:J#+4^#il#ffl#J 


Tf 


-ef- 


3X 


XE 


3X 


XE 


J^      - 
5      4 


-fir    b     5 
5     ^     If 


In  the  first  of  the  above  examples  the  seventh  moves  first,  after- 
ward the  bass  and  other  voices.  In  the  second  example  the  bass 
moves  first,  and  with  it  the  voice  that  moves  into  octave  with  the 
bass,  afterward  the  seventh  and  the  one  remaining  voice.  The  bass 
can  move  alone,  as  in  the  first  example  the  seventh  does,  but  the 
form  of  the  resulting  chord  (3)  can  be  understood  only  when  we 
reach  Suspension  (Chap.  XIII).  According  to  the  above,  which  is 
the  more  usual  method  of  resolving  this  chord,  each  voice  moves  a 
semitone;  the  root  upward,  the  other  three  voices  dozvnivard. 
There  is  no  law,  excepting  the  requirement  of  the  ear ;  and  the  pupil 
is  advised  to  play  the  above  resolution  carefully,  and  then  see  if  he 
can  satisfactorily  make  either  of  the  voices  move  in  *•*  '^'rection 
more  than  a  .semitone. 

The  other  method  of  avoiding  the  parallel  fifth  is  by  means  of 
the  following  progressions,  which  are  les>^  pleasing  and  quite  un- 
usual : 


CHAPTER  XII. 


119 


? 


3X 


-O 


m 


33: 


T^      15^ 


^ 


# 


« 


-4ir 
5 


7 

tl5 


^6^ 
5 


a 


^^ 


6    7 


All  the  facts  concerning  the  chord  of  the  augmented  sixth-  and- 
afth  have  been  illustrated  by  the  use  of  a  single  chord  of  that  sort. 
But  as  stated  at  the  beginning,  any  minor  triad  with  perfect  fifth, 
its  root  raised  a  semitone  and  the  seventh  added,  will  give  us  the 
same  effect  in  its  first  inversion.  Every  scale  has  three  minor  triads 
with  perfect  fifth,  viz.,  on  the  second,  third  and  sixth  of  the  scale, 
illustrated  in  the  C-scale  thus : 


^ 


^§ 


g 


Raising  the  root,  adding  the  seventh,  taking  the  first  inversion, 
and  resolving  according  to  the  usual  method,  the  procedure  in  the 
case  of  each  of  these  is  as  follows: 


i^ps 


XE 


xs: 


* 


o 


-o- 


XE 


8^^ 


JDE 


13: 


~o~ 


or 


_o_ 


m 


3ci: 


-^ 


XE 


i 


5 


4 
3 


3. 


fr"-^  \hH 


xr 


XE 


i 


5^^ 


« 


-o- 


ii: 


-6- 
5 


or 
J2 


XE 


XE 


XE 


¥ 


5 


#5 


5 


3 


^ 


ff^*  itfy; 


-cv 


« 


XE 


XE 


^^    >« 


JOL 


xs: 


rrr 


ii 


S 


XE 


ZDl 


-O- 


XE 


^ 

6    ■ 

-fir 

-«r 

-ft- 

-5- 

5 

4 

# 

5 

1 

# 

120 


FARKHURST  HARMONY. 


Let  the  pupil  take  the  triads  on  the  second,  third  and  sixth  of  each 
of  the  following  scales  (G,  D,  F,  Bb),  develop  the  chord  of  the 
augmented  sixth-and-Hfth,  with  its  resolution,  and  place  underneath 
the  proper  figuring,  as  in  the  above  example.  Only  by  such  a  pro- 
cess can  complete  mastery  of  this  chord  be  obtained. 

Exercises. 


# 


*l^ 


-*>^ 


J3L 


6  ^ 


4     2 


6    -6- 


m 


1        -4T  It       W* 


£ 


4    $ 


i 


35: 


5 


4  ^ 


§ 


^ 


-o- 


^ 


3t 


TIT 
5 


.11 


ll6    4 
5    3 


4 


4. 


§ 


rzB: 


s 


zz 


6    BT^ 
5    « 


5. 


5     4 


2 


P 


a 


^5 — lF-% 


XE 


A    87 


i 


6       ft 


6" 


^  6 
5    4 


^  n 


In  the  last  illustration,  three  chords  of  the  augmented  sixth-and- 
£fth  are  exhibited,  derived  from  three  minor  triads  of  the  C-major 
scale;  but  no  one  of  them  resolves  into  an  unequivocal  C  major 
chord,  and  the  second  and  third  have  a  resolving  chord  that  is  thor- 
oughly foreign  to  C-major  as  to  be  unsuitable  for  that  scale.  The 
first  of  the  three  will  be  seen  to  resolve  into  the  dominant  of  the 
relative  minor  scale. 


m 


ICEZZZXE 


3tr 


JOL 


-CV^ 


m 


s 


-€>- 


-6- 
5 


XE 


and  usually  finds  employment  in  this  connection.  The  other  two 
similarly  resolve  into  what  may  be  taken  as  the  dominant  of  a  minor 
scale,  but  very  remote  from  C-major;  and  thus  this  chord  of  the 
augmented  sixth-and-Hfth,  serving  as  a  connecting  link  between  re- 
mote scales,  is  frequently  used  in  modulation  (See  Chap.  XVIII). 


CHAPTER  XIL 


12t 


4th.     The  Chord  of  the  Augmented  Sixth- Fourth-and-Third. 
The  chord  of  the  seventh  on  the  seventh  degree  of  the  scale,  with 
its  third  raised,  gives  us  the  following: 


^3 


r^tftr^H^^'-'^''^""  '^^"^  ^^^'  s 


7  7 


o    .    o 


m 


-^ 


xn 


31: 


4 
3 


4 
3 


It  will  be  observed  that  this  chord  is  formed  on  the  remaining 
minor  triad,  the  other  three  being  used  in  forming  the  chord  of  the 
augmented  sixth-and-Hfth. 

Of  these  forms  only  the  second  inversion,  the  chord  of  the  aug- 
mented sixth- f our th-and-third,  is  practicable,  but  this  is  pleasingly 
characteristic  and  effective.  It  differs  not  at  all  in  its  construction 
JFrom  an  ordinary  chord  of  the  fourth-and-third  (second  inversion), 
except  that  the  sixth  from  the  bass  is  augmented  instead  of  being 
major  or  minor,  and  the  resolution  is  strictly  regular.  But  there  is 
ia  combination  of  intervals  in  this  chord  which  distinguishes  it  from 
every  other,  and  it  should  be  studied  until  it  can  be  readily  distin- 
guished from  the  ordinary  fourth-and-third  chord.  To  this  end  let 
i^he  pupil  develop  this  chord  after  the  manner  of  the  above  illustra- 
tion, on  the  seventh  degree  of  the  different  major  scales,  and  resolve 
it,  noticing  that  in  the  resolution  the  5th  (i.  e.,  the  bass)  and  the  7th 
descend  a  minor  second  (a  semitone),  and  the  3rd  (which  is  the 
augmented  sixth;  from  the  bass)  ascends  Or  minor  second,  while  the 
root  remains  stationar}\ 

The  two  chords,  the  augmented  sixth-and-Hfth,  and  the  aug- 
mented sixth-fourth-and-third,  are  so  nearly  alike  in  sound  to  the 
unpracticed  ear,  and  yet  so  radically  different  in  their  construction, 
that  it  is  well  to  bring  them  into  comparison  in  the  following  manner: 


^^ 


XE 


33: 


33: 


35: 


^V 


i 


^^ 


33L 


^^ 


^ 


•¥- 


3X 


-fr 

rt 

5 

-fr 

5 

4 

# 

4 
3 

122 


PARKHURST  HARMONY. 


The  two  chords  above  differ  only  in  one  tone,  and  the  ultimate 
resolution  of  the  two  is  the  same,  but  the  root  of  the  first  is  D,  and 
the  root  of  the  second  is  B. 

In  the  following  exercises  let  the  pupil  determine  which  of  the 
sixth' f our th-and-third  chords  have  an  augmented  sixth,  and  which 
of  them  have  only  a  major  sixth. 


Exercises. 


5 


5S: 


o- 


131 


2. 


f 


'i    6 


r       '  U    \Ar 


4     i 


m 


3   fi 


-fS- 


30r 


1 


-€»- 


r.     ^      '  **_    '  ^ 


3    - 

open  position 


7— T 


3. 


6T 


^^ 


S 


E=3Z 


4     *^        3    4 


g   I /-J  gHig 


jH 


5  # 


4. 


^ 


open,  position. 


^pr-15 


i 


pep 


XE 


:si: 


^«>^ 


^  -tir       «   5 

4        4    3 


^ 


^ 


4 
8 


-«>■ 


-«>- 


54        <»      4 
3  3 


^ 


^ 


-tt-  K  1/7  '■  fi" 


4     tf 


5th.     The  Diminished  Triad  with  Major  Third. 


I 


^ 


m. 


XE 


This  is  not  of  service  in  four-part  harmony,  as  neither  of  the 
intervals  admits  of  two  progressions,  and  therefore  cannot  be 
doubled ;  and  in  three-part  harmony  it  is  of  use  only  when  the  voices 
are  dispersed  in  this  manner, 


I 


«♦- 


CHAPTER  XII. 


123 


Its  use  can  be  illustrated  thus : 


^ 


XE 


i 


^^=g 


^8r 


4 


XT 

6 


1^ 
6 


If 


-^    5 


The  following-  will  assist  the  memory  in  regard  to  these  difficult 
■"altered  chords." 

Every  triad  in  the  major  scale  is  at  the  foundation  of  an  "altered 
■chord."  From  the  three  major  triads  (on  ist,  4th  and  5th  degrees). 
we  get  the  chords  with  augmented  fifth ;  from  the  four  minor  triads 
(on  2d,  3rd,  6th  and  7th  degrees)  we  get  the  chords  with  aug- 
mented  sixth;  using  the  first  three  for  the  chords  of  augmented 
3txth,  and  of  augmented  sixth-and-Hfth,  and  the  remaining  one  (on 
the  7th  degree)  for  the  chord  of  augmented  sixth-fourth-and-third, 
thus: 


4 


^ 


i: 


|«»R- 


I a  n«'y  itf-^  ||»|T  I 


1       f 


For  an  explanation  of  the  method  of  determining  how  a  g^ven 
distance  is  to  be  named,  as  for  example  an  augmented  sixth  or  a 
minor  seventh,  an  augmented  fourth  or  a  diminished  fifth,  etc.,  see 
Appendix  (I). 

Beyond  these  five  incidental  re-formations  of  our  two  elementary 
harmonies  (the  common  chord  and  the  seventh-chord)  there  are  no 
others  that  are  to  be  ranked  among  the  fundamental  harmonies. 

And  in  regard  even  to  these  five  "altered  chords,"  which  are  cer- 
tainly striking  in  their  effect,  it  should  be  observed  that  the  substan- 
tial merit  of  any  composition  depends  not  to  any  great  degree  upon 
the  startling  effect  of  strange  harmonies,  but  mainly  upon  the  ar- 
tistic use  of  the  simple  and  familiar  chords. 

Chords  are  the  words  of  music,  and  the  deepest  thoughts  of  any 
language  find  their  best  expression  in  the  simplest  terms  of  that 
language. 

It  is  however  incumbent  upon  the  author  of  such  a  treatise  as 
this  to  acquaint  the  pupil  with  all  his  w^orking  material,  that  he  may 
be  fully  equipped  for  every  emergency.    At  the  same  time  this  is  a 


124  PARKHURST  HARMONY. 

most  opportune  occasion  for  reminding  the  prospective  composer  of 
a  fact  he  can  never  afford  to  forget,  namely,  that  when  an  author  can 
find  nothing  new  and  true  to  say,  he  only  cheapens  his  art  by  resort- 
ing to  the  startling. 

After  the  foregoing  study  of  all  the  fundamental  chords  the 
pupil  is  in  a  position  to  appreciate  the  classification  of  those  chords 
into  the  independent  and  the  dependent,  as  made  upon  page  14.  The 
common  chords  in  general  constitute  the  independent  chords,  as  in- 
volving no  definitely  fixed  progression.  This  is  pre-eminently  true 
of  the  fundamental  position  and  the  first  inversion  of  the  common 
chords ;  whereas  the  second  inversion,  the  J  chord,  by  reason  of 
the  interval  of  the  fourth  which  it  contains,  has  in  it  something  of 
the  quality  of  a  discord,  and  is  thus  followed  most  naturally  and 
commonly  by  the  third  (as  it  were,  the  resolving  tone  of  the  fourth). 
The  second  inversion  of  the  common  chord  is  certainly  the  least  in- 
dependent, and  is  closely  allied  to  the  dependent  chords,  which  have 
inherently  a  fixed  progression,  and  comprise  the  seventh-chords 
(fundamental  and  inverted)  and  the  altered  chords.  In  other  words, 
the  independent  chords  are  the  concordant,  the  dependent  chords  are 
the  discordant. 

Summary. 

Three  ways  in  which  chords  are  altered  by  accidentals: — How 
many  characteristically  altered  chords: — The  terms  that  character- 
ize the  three  sorts  of  altered  chords : — Formation  of  the  augmented 
triad: — Where  it  occurs  in  the  minor  scale: — On  which  degrees  of 
the  major  scale  serviceable: — In  what  way  augmented  interval  is 
commonly  introduced  : — Effect  of  augmented  fifth  in  minor  triads: — 
Use  of  augmented  triads  in  inversions : — Addition  of  seventh  to  the 
three  augmented  triads: — Comparative  effectiveness  of  these  three 
seventh-chords  in  their  inversions: — Formation  of  augmented  sixth 
chord: — Distinction  between  sharped  sixth  and  augmented  sixth: — 
Invariable  progression  of  augmented  sixth: — Which  of  the  minor 
triads  can  be  used  to  form  augmented  sixth  chords : — Which  interval 
only  can  be  doubled,  and  why : — ^^Formation  of  augmented  sixth-and- 
fifth  chord: — Problem  in  its  resolution: — Solution  of  problem: — 
The  natural  interval  of  progression  of  each  voice,  moving  from 
this  chord: — Which  of  the  triads  of  the  scale  can  be  used  to  form 
this  chord: — Comparison  of  the  three  sixth-and-fifth  chords  of  a 
scale,  as  r^.gards  the  relation  of  the  resolving  chords  to  the  scale : — 
A  serviceable  chord  for  modulation: — Formation  of  augmented 
sixth- fourth-and-third  chord  : — Diminished  triad  with  major  third, 
when  serviceable: — The  seven  successive  triads  of  the  scale  at  the 


CHAPTER  XII. 


\T^ 


foundation-  of  what  "altered  chords" : — The  merit  of  a  composition 
dependent  chiefly  upon  what: — Meaning  of  independent  and  de- 
pendent, as  applied  to  chords,  and  what  chords  are  comprised  in 
each  class. 

Figure  the  basses  of  the  following  Exercises. 


fl^^^^^ 


I"  i|i  iii'ii" 


'yi-ix 


p 


^.;-'ij  f"irJiiMri;f^ 


M 


I  iii  iriTiiif  I  \\\\v\^\  Ti 


i'Jj||ii.jt'Jiij 


m 


r* 


Wf 


XT 


i 


w 


^^ 


i=t 


^^ 


p 


ff 


i'iiii'iJJiJJUi^iiJ^ 


jJ'V^i'rr'rrir 


lJ-^ 


m^ 


^rr'r  rr'r  rr'i'  '^"^fff 


|'-lH-|r'VMJ,ll''ll(^ 


JiJjJiMJj 


J 


■^•>f  frri»f  r^||.^7^l^''^l^'^r^i-J^tP 


126 


PARKHURST  HARMONY. 

9. 


i 


v^''j|tfMf^HW^rrr(',irff'^ 


10. 


fe 


s 


F^ 


f 


rff 


r 


':;^^,i;,,.,fj'j;.g.*ii 


'Mr     I  r  r  «r  »r  jA^^^^ 


^ 


y't'T )'  rU.J 


^^ 


2z: 


V27 


PART  II. 

':he  auxiliary  chords. 

The  chords  which  have  thus  far  engaged  our  attention  are  the 
/nost  important,  as  being  the  fundamental  harmonies.  They  consti- 
tute the  harmonic  basis  of  all  musical  composition.  They  are  the 
skeleton,  solid  and  substantial,  by  whose  firm  continuity  the  whole 
structure  is  made  coherent.  But  while  in  rare  instances  a  whole 
composition  (but  of  necessity  very  brief)  may  be  developed  out  of 
these  fundamental  harmonies — as  hymn  tunes  in  choral  style,  like 
"Old  Hundred" — the  outlines  of  such  a  form  of  composition  are  evi- 
dently too  rigid  and  angular  for  prolonged  use.  While  "fundamen- 
tal harmonies" — the  bone  and  sinew  of  the  composition — can  never 
relegate  their  peculiar  functions  in  what  may  be  called  the  anatomy 
of  music,  it  is  no  disparagement  of  their  importance  that  they  must 
be  clothed  upon,  to  insure  a  becoming  grace.  To  afford  lowing 
outlines,  as  well  as  infinite  variety,  where  else  we  should  be  soon  op- 
pressed with  an  ungainly  and  repulsive  austerity  and  endless  mon- 
otony, is  the  function  of  the 

Auxiliary  Chords, 

forming  the  rounded  fleshly  covering  that  gives  constant  proof  of, 
yet  at  the  same  time  gracefully  conceals,  the  skeleton  beneath.  It 
is  like  the  drapery  that  takes  form  from  the  very  figure  it  hides. 
These  auxiliary  effects  may  be  classed  as  follows : 

1.  Auxiliary  Chords. 

(a)  Suspension  chords. 

(b)  Auxiliary  Chords,  other  than  "suspension  chords,"'  to  be 

described  hereafter  in  detail. 

2.  AuxiLiAR  Tones,  of  various  sorts,  and  known  as  passing 

tones,  appogiaturas,  grace  notes,  etc. 
A  so-called  "auxiliary  chord"  is  usually  a  combination  of  tones 
belonging  to  a  "fundamental  chord"  with  other  tones  foreign  to 
that  chord,  so  that  we  can  speak  of  the  e?itire  combination  as  an 
auxiliary  chord,  or  speak  only  of  those  single  tones  in  the  combina- 
tion which  are  foreign  to  the  fundamental  chord,  in  that  case  call- 
ing them  auxiliary  tones.  Thus  we  can  call  the  following  harmony 
an  auxiliary  chord,  or  speak  of  the  soprano  (d)  as  an  auxiliary  tone 
combined  with  the  common  chord  of  C. 


1 2^5 


PARKHURST  HARMONY. 


i 


^ 


4): 


The  foregoing  furnish  all  the  Accessory  Harmonies  wherewith 
the  Fundamental  Harmonies  may  be  embellished  ;  and  the  knowledge 
of  both  sorts,  Fundamental  and  Accessory,  makes  possible  the  full 
analysis  of  all  chords. 

The  several  accessory  effects  given  above  must  now  be  studied 
separately. 

CHAPTER  XIII. 

Suspension. 

Hitherto  the  movement  of  all  the  voices  from  one  chord  to  the 
next  has  been  simultaneous.  But  under  certain  conditions  one  or 
more  of  the  voices  can  be  delayed  on  their  tones  in  the  first  chord, 
while  the  remaining  voices  move  to  their  places  in  the  following 
chord.  The  result  is  a  mixed  chord ;  i.  e.,  it  is  a  combination  of 
tones  of  which  one  part  belongs  to  one  chord,  and  the  other  part  to 
the  other  chord.  The  tones  that  are  thus  held  over  from  the  pre- 
vious chord  are  said  to  be  suspended.    In  the  following, 


^ 


58; 


XF 


3£ 


« 


^ 


3r 


instead  of  having  the  soprano  move  to  B  at  the  beginning  of  the 
second  measure,  it  can  delay  upon  C  until  the  last  half  of  the  second 
measure,  thus: 


i 


^ 


m 


XT 


Vy^S 


s 


xz: 


The  pupil  must  clearly  distinguish  between  suspension  and  mere 

retention  of  a  tone.  Two  chords  often  have  a  tone  in  common,  which 

is  then  simply  retained,  and  belongs  as  much  to  the  second  chord  as 

vto  the  first.    Thus  G,  in  the  above  example,  is  common  to  all  three 

•chords ;  but  C,  in  the  first  half  of  the  second  measure,  does  not  be- 


CHAPTER  XIIL 


129 


long  to  the  second  measure  (which  belongs  to  the  chord  of  G)  and 
is  foreign  to  the  prevaiHng  harmony.  The  proper  tone  of  the  har- 
mony for  soprano  is  B.  The  characteristic  quahty  of  a  suspension, 
making  it  effective,  is  the  discordant  relation  of  the  suspended  tone 
to  the  true  harmony  of  the  measure. 

There  are  three  sorts  of  resolution,  according  to  the  movement 
of  the  voice  from  the  suspended  tone  to  the  next,  viz., 

(i)     Resolution  downward. 

(2)  Resolution  upward. 

(In  these  two  sorts  the  voice  moves  by  one  diatonic  de- 
gree down  or  up.) 

(3)  Free  resolution  (to  be  explained  later). 

(i)     Resolution  downwaeld. 

This  method  of  resolution,  in  which  the  suspended  tone  leads 
to  the  next  degree  below,  is  by  far  the  most  common,  as  it  is  the 
inherent  tendency  of  every  discordant  tone  to  lead  downward  to  a 
concord.  In  the  second  sort  of  suspension  we  shall  find  that  other 
considerations  are  involved,  which  counterbalance  the  natural  down- 
ward tendency,  and  induce  an  upward  movement. 

By  the  very  nature  of  the  case,  the  suspended  tone  is  heard  in 
the  previous  chord ;  it  is  therefore  prepared,  and  the  natural  law  of 
discords  requires  also  that  it  be  resolved  by  leading  downward  one 
degree. 

The  simple  law  of  suspension  is — 

Every  suspension  must  be  prepared  and  resolved,  and  in  the 
same  voice. 

'  Inasmuch  as  any  tone  of  a  chord  can  be  suspended,  if  it  can  only 
be  properly  resolved  in  the  next  chord,  it  follows,  inversely,  that  we 
can  have  a  suspension  above  each  component  tone  of  a  chord,  pro- 
vided that  the  tone  above  it  belongs  to  the  previous  chord.  Thus  we 
can  have  a  suspension  above  the  8th,  or  the  5th,  or  the  3rd,  or  the 
ist  (i.  e.,  the  bass  tone)  ;  or,  in  other  words,  we  may  have  a  suspen- 
sion of  the  ninth,  of  the  sixth,  of  the  fourth,  and  of  the  second,  as 
follows: 


33: 


W=f 


^ 


^ 


9th 


6th 


XT 

4th 


2nd 


3 


^ 


33: 


XE 


XE 


-9 — w 


-V 


7       W 

4      5 

a     3 


130 


PARKHURST  HARMONY. 


Of  course,  some  suspensions  are  more  effective  and  more  fre- 
quently employed  than  others,  but  it  is  our  present  purpose  to  dis- 
cover all  possible  suspensions,  and  in  regard  to  those  that  appear 
least  serviceable,  there  are  circumstances  that  may  justify  and 
even  require  their  use. 

As  before  remarked,  the  characteristic  feature  of  a  suspension  is 
its  discordance  with  the  prevailing  harmony.  But  in  the  suspension 
of  the  sixth. 


^ 


r 


^ 


3x: 


6     5 

the  suspended  tone  does  not  produce  that  effect,  and  the  combination 
may  be  analyzed  as  simply  a  chord  of  the  sixth  followed  by  a  com- 
mon chord  on  the  same  bass  tone.  Any  isolated  case  like  the  above 
would  more  naturally  be  treated,  not  as  a  suspension,  but  as  a  verit- 
able sixth-chord ;  but  when  it  occurs  in  a  series  of  suspensions,  the 
most  intelligent  analysis  would  find  a  suspension  in  this  chord  also. 
Thus  in  the  following, 


^^ii'iUliJ 


2Z 


^ 


■o- 


xz: 


-o- 


xr 


XE 


IB — 5" 


r^ — 3- 


it  is  plain  that  the  ruling  harmony  of  each  measure  is  that  which  is 
formed  in  the  last  half  of  each  measure,  and  by  omitting  the  suspen- 
sion, the  fundamental  harmony  is  as  follows: 


$ 


^=f=a 


m 


-*>- 


§-mj^^_Ui 


^ 


xz: 


xn 


-•V- 


xin 


6 
6 

so  that  in  the  second  and  fourth  measures  we  should  properly  treat 
the  sixth  as  a  suspension.    We  shall  find  other  instances  of  concord- 


CHAPTER  XIII. 


131 


ant  suspension,  where  we  must  judge  by  the  circumstances  whether 
it  be  a  genuine  suspension. 

We  will  now  treat  of  each  suspension  singly. 

Suspension  of  the  Ninth. 
This  can  occur  in  cither  of  the  three  upper  voices,  thus : 


^^ 


^S 


xr 


zz: 


f 


«^ 


-*»- 


XE 


XE 


XE 


"sr 


It  will  be  found  more  satisfactory  in  soprano  or  alto  than  in  tenor, 
for  the  reason  that  the  discordance,  being  between  the  suspended 
tone  and  the  bass,  is  not  so  conspicuous  when  one  or  more  tones,  in 
concordant  relation  to  the  bass,  intervene  between  the  discordant 
tones,  which  draw  the  attention  from  the  discordance.  When  the 
suspension  is  in  the  tenor,  there  can  be  no  intervening  tone  to 
soften  the  effect. 

Heretofore  no  distinction  has  been  made  between  the  ninth  and 
tlie  second,  and  essentially  they  are  the  same.  But  by  the  remove  of 
one  or  more  octaves  the  harshness  of  the  discord  is  mitigated — di- 
luted by  the  distance.  The  suspension  of  a  second,  resolving  into 
unison,  like  the  following 


m 


^ 


-♦>■ 


xz: 


rfT 


m 


XE 


g 


^E>- 


is  not  endurable.    The  same  objection  exists  to  a  similar  suspension 
in  the  tenor, 


P 


XE 


M 


^J«i 


but  in  less  degree,  because  the  combination,  being  at  a  lower  pitch, 
is  less  shrill.  While  unsatisfactory  if  it  resolves  into  unison,  such 
a  suspension  of  the  second  in  the  tenor  is  admissible,  if  the  bass 


32 


PARKHURST  HARMONY. 


moves  away  from  the  tone  into  which  the  tenor  resolves,  thus 


M 


-€>- 


^ 


S 


The  figuring  of  the  suspension  of  the  ninth,  with  its  resolution. 

The  procedure  in  writing 


9    8 

is  usually  9  8,  abbreviated  from    5  - 
this  chord  is: 


First  Hud  the  ninth  above  the  bass,  put  it  in  the  same  voice  in 
which  that  tone  occurred  in  the  preceding  chord,  then  put  in  the 
third  and  the  fifth  of  the  chord  that  is  founded  on  the  bass  tone. 


Illustration. 


bd.MT^^ijL.,   JTiJ 


SI 


j^^l^ij 


1SZJS 


^ 


T^ 


98  6     98       6    98  87    98  7 

5.  \>b. 

Exercises. 


7  8  6   9    s.-^ 


xr 


« 


1. 


17   '        6 — te-7 


§  '   9^8'»' 


Xfl 


^-^ 


t>  5     9  8 


2. 


yf 


3D[ 


XE 


«  7      .9  8       6-       9  S     6    6       t>       *> 


l»5 


9    87 


s 


8-  open  position. 


i 


^ 


XE 


jDE 


«     I   «' 


6 


98      g 


9   8      6 


4.  open  position. 


w 


^^^m 


t 


T     98       4  3^ 


a  '  o 


XT 


6 
5.  close  position 


64 


9  8^     98 


m 


5^ 


1^ 


fc  '6      l» 


XE 


«     87 


XE 


<g-B^ 


-g-F 


5 


98 


CHAPTER  XIIL 


133 


Sight-reading. 

With  inversions  of  the  dominant-seventh. 
1. 


'y-H  {'f\'\-{^'\ 


P 


f 


-o- 


5 


^2r-^ 


2. 


6  4 
3 


^-T 


3 


IX 


f 


3 


3. 


6     4 
3 


m 


zz 


if 


p 


"BIT 


IE 


8  7 


4. 


^ 


fczz 


ZE 


4   li 


2;     fBr-T" 

3 


6    C' 
4    8  7 


Suspension  of  the  Ninth  in  First  and  Second  Inversions. 
It  is  evident  that  the  same  tone  can  be  suspended  in  the  inver- 
sions as  in  the  fundamental  position ,  thus : 


I 


JT^  J II  Jt^  ,\  11 J^ 


¥ 


xx: 


xx: 


■^-"B" 


s 


i-~w 


XE 


5  A 


Suspension  of  the  Ninth  in  First  Inversion. 
We  have  before  seen  that  we  can  double  either  the  root,  third 
(occasionally)  or  fifth,  in  the  first  inversion. 


f#^ 

-TT- 

=WI 

TT 1 

4y 

1 

_lf_ 

"n 

,...,^.,J 

■6 

S-" 

by  doubling  the  root  we  get  one  form  of  the  chord  in  suspension, 
by  doubling  either  third  or  iifth  we  get  a  slightly  different  form, 
thus; 


i  JT^_  J II JT^,  J II  ^up"  FFi=^ 

(CP    p      I   o  II    Q      I   o  li    g-^l   o    — hI  g     I 


XI- 


-o- 


Ar-1^ 


i 


XE 


S 


i 


XE 


XE 


-1 — w 

6. 


"7 6" 


134 


PARKHURST  HARMONY. 


The  figuring  of  the  two  forms  is  given  above.  The  second  form 
might  be  analyzed  as  a  simple  chord  of  the  seventh,  on  E,  with  omis- 
sion of  the  fifth  (B)  ;  and  whether  it  is  to  be  construed  as  a  verit- 
able seventh-chord,  in  fundamental  position,  or  as  a  suspension  of 
the  ninth,  in  the  first  inversion,  must  be  determined  by  the  circum- 
stance, whether  it  occurs  in  a  series  of  suspensions  or  not.  Thus 
in  the  following  it  is  reasonable  to  interpret  the  seventh-chord  as  a 
suspension  of  the  ninth,  in  first  inversion. 


because  occurring  in  a  series  of  suspensions,  so  that  the  ruling  har- 
monics of  the  above  measures  are  as  follows : 


^ 


XE 


^ 


^ 


XE 


tr 


351 


§ 


55^ 


ax 


XE 


XE 


'W 


Illustration. 


rrfr^' 


m 


u 


X 


^ 


xc 


H 


i! 


-€>- 


rf 


"5—^ 


-T~cr 


T 


4 


CHAPTER  XIII. 


135 


Exi-:Reisi:s. 


^l,     ts^ 


s 


P 


-O^ 


^ 


8    7      9  H      7  t> 
2.  open  position. 


jDC 


^^^=22 


ST  8        "7    6 


Xfl 


XE 


1^ «r^ 

3.  close  position. 


-W^ 


F~8r     7~15" 


m 


-^ 


3z: 


zz: 


-g-7      g~7       9^76 
4.    open  position.. 


6    8   7 


i 


XH 


XE 


3 


XE 


6 7  6      6  -        b   b      o^ 

iS  _  5        4    8       7  6 


g;       o — 

6         .8    7 


m 


5.    open  position 


:tli 


^ 


f 


4 
3 


xi: 


7^ 
6 


6        6  7 


6.   open  position. 


xn 


^ 


^m 


XE 


(g   Pig 


F6 7   B      'id    Ijl        6    ^6        y  8     '6    5^ 

4      6  5  4    7 

SUSTM'XSION-    OF    THE    NiNTH    IN    SeCOND    TxVERSION 


i 


JtjJiiJtJj 


«^ 


« 


«ir 


XE 


i^i^ 


g 


XE 


-w-^ 


XE 


"6~^ 
5  4 


XE 


"6      ^ 
5      4 


f 


XE 


5  4 


This  is  a  very  common  and  effective  suspension.  As  in  the  chord  of 
J,  it  is  better  to  double  the  fifth  (i.  e.,  the  bass  tone),  the  same 
holds  good  when  the  suspension  of  the  ninth  is  introduced  into  this 
chord,  as  in  the  example  above.  The  doubling-  of  the  root  in  the 
chord  of    J    is  usually  to  be  avoided,  as  harsh ; 


m 


*v.  *>  4 


§ 


36 


PARKHURST  HARMONY, 


but  the  melodic  progression  of  the  voices  sometimes  makes  it  de- 
sirable, as  in  the  following: 


Similarly,  the  doubling  of  the  root  in  this  chord  of  |  with  a  sus- 
pension of  the  ninth  is  still  more  harsh,  as  the  suspension  and  its 
resolving  tone  (an  octave  distanct)  are  heard  simultaneously; 


I 


ib^^ 


-€>- 


m 


XE 


6— :zr 
5  C 
4. 


but  melodic  considerations  can  also  make  this  desirable: 


i 


w 


33r 


JDL 


-€^ 


^ 


6   - 
5    4 


7    - 
4    3 


The  figuring  of  the  suspension  of  the  ninth,  in  the  second  in- 
version, is  6^  which  is  to  be  carefully  distinguished  from  our  previ- 
ous I,  which  signifies  the  first  inversion  of  a  seventh-chord;  for  the 
analysis  of  our  present  combination  shows  it  to  be  a  common  chord, 
with  the  root  a  fifth  below,  and  with  a  foreign  element  (the  sus- 
pended tone)  in  it.  Inasmuch  as  we  shall  find  several  other  sus- 
pension-chords, whose  figuring  is  identical  with  that  of  some  of  the 
chords  already  learned  in  Part  I  (the  fundamental  harmonies),  but 
utterly  different  in  their  nature  and  progression,  it  is  in  general 
inadvisable  to  name  the  suspension-chords  from  their  figuring. 
There  are  only  three  exceptions  to  this : — the  suspension  of  the  ninth 
and  suspension  of  the  fourth,  in  their  fundamental  position,  are 
called  the  chord  of  the  ninth,  and  chord  of  the  fourth.  Also  the 
suspension  of  the   fourth   in   the  bass  is  called  the  chord  of  the 


CHAPTER  Kill. 


137 


Hfth-and'second..  The  remaining  suspension  chords  are  indicated 
by  giving  the  name  of  the  suspension  as  in  its  fundamental  position, 
and  adding  the  inversion  as  the  case  may  he.  The  suspensions 
thus  far  considered  are  therefore  named  as  follows: 


Chord  of  the  Ninth. 


i 


^ 


^ 


^^ 


Suspension  of  the  Ninth,  First  Inversion, 


I 


^^B 


^7~6" 


xr 


7    6 
6 


Suspension  of  the  Ninth,  Second  Inversion. 


I 


JtJ  -I  I J  I J  -i 


C 

^ 


XE 


6    - 
5   4 


XE 


6   - 
5  4 


This  manner  of  naming  them  affords  the  only  complete  analysis 
of  the  chords,  and  is  by  far  the  simplest. 

With  the  figures  |  ~  the  suspension  of  the  ninth,  second 
inversion,  can  be  written  in  either  of  the  above  given  forms,  al- 
though there  is  no  figure  to  account  for  C  in  tenor  of  second  form. 
But  in  writing  this  C,  although  not  expressed  in  the  figuring,  we  are 
not  at  all  violating  the  nature  of  the  chord.  Intelligent  harmoniz- 
ing must  rise  above  the  mere  matliematical  calculation,  and  grasp 
the  inner  nature  and  spirit  of  the  chords. 


138 


PARKHURST  HARMONY. 
Illustration. 


ilT,W^i|,j-'ivJi'J|J^ 


fffr"  ■f^j.rf 


8=* 


_i — t     1 1„ 


m 


■o- 


3z: 


XE 


g 


XT 


T^ 


IT 


2~^K^ 


•3   B       6   - 
5   4 


Exercises. 


^ 


zzz:^ 


^ 


^6~^       9  8       6  -        9  8      W 
i>  5 


T^Y 


£ 


XE 


3 


3. 


'  t 


~7~W 


2     6 


^ 


XH 


3      ^ 


6 


54 


8    7 


s 


22=^ 


s — ^ 


5  4 


^»- 


5.    open  position 


6  7 

4  ^ 


^ 


*f 


^ 


y  «  t 


-^ — 

9  8 


^  "5 

6.      open  and  close 


8    7 


^ 


XE 


zz=?z 


a 


-^>- 


5    '^7    '    «  H  '  7     «     ■  9  8    '  g    e        ^^       «   '7 


^ 


s^ 


XE 


4  ^        «  7 


4 
3 


S 


8.   open  position, in  score. 


i 


«        «7 


5  f?  98  6       98  7 

5  ^ 


6       987  ^6  ^?^.^ 


67     6  5 


XT 

987 


The  suspension  is  merely  a  rf<?/av  in  the  progression,  and  there- 
fore no  progression  can  be  allowed,  in  the  use  of  suspension,  which 
would  be  incorrect  without  the  delay.  Thus  the  following  are 
faulty, 


CHAPTER  XIII. 


139 


octave. 


fifth, 


^m 


M 


XE 


:C^ 


m 


^m- 


-A-^J. 


3z: 


because  the  octave  and  fifth  are  inadmissible  without  the  suspension, 
thus : 


^ 


P    |o  t 


^ 


-O- 


-f^  <^ 


m 


f 


:sje: 


jOl 


Sight-reading. 
With  secondary-seventh  chords. 


1. 


i 


«- 


^ 


XE 


2. 


s 


i 


§  7 


j»  j  ^^  1 1;  N  j  r  '  o  II 


e: 


^ 


XE 


-O — 

8   7 


5        8  7 


*  I 


6  7"^ 

4 


^ 


§ 


XE 


-€> 


3         6   5 


5. 


m 


m 


t5 


4      ' 


I3      7     7 


3 


6 


6       6     7 
4 


Suspension  of  the  Sixth. 

Fundamental  position. 


ij^^J^ 


IE 


1?!^ 


^ 


XF~ 


~6~T 


^:^ 


XE 


40 


PARKHURST  HARMONY. 


In  its  construction  this  does  not  differ  at  all  from  a  chord  of  the 
^ixth,  and  not  being  a  discordant  suspension,  will  be  regarded  as  a 
suspension  only  in  a  series  of  such  chords,  thus: 


*fs 


i^  'li  ni  ni  h^^ 


^ 


JOL 


XE 


XE 


6      5 


4,      3 


4     3 


The  ruling  harmony  of  each  measure  is 


#'roN§iyi§ 


H 


i 


XE 


XE 


XE 


This  chord  needs  no  special  illustration  nor  exercises. 
First  inversion. 


^    i^^-S- 


m 


XE 


m 


p 


3nr 


XE 


t   i 


f 


x6     - 
4^3 


In  its  construction  this  does  not  differ  at  all  from  a  chord  of  the 
sixth-and-fourth.  and  will  therefore  be  regarded  as  a  suspension  only 
in  a  series  of  such  chords.  No  special  illustration  nor  exercises 
are  necessary. 

Secoond  inversion. 


r  1.— I    I 


^ 


xe: 


XE 


^^=^=^-^ 


^  « 

4*: 


8 


-€>- 


*      3  %     - 

9 

The  figuring  of  this  chord  is  6  but  the  pupil  must  be  careful  not 
to  call  it  a  suspension  of  the  ninth,  although  the  suspended  tone  is  a 
ninth  from  the  bass,  but  should  recognize  in  it  the  suspension  of  the 
sixth,  in  the  second  inversion. 


CHAPTER  XIIL 


141 


Suspension  of  the 
Sixth. 


Suspension  of  the 
Sixth,  first 
inversion. 


Suspension  of  the 

Sixth,  second 

inversion. 


m 


T 


^ 


th 


3 


IZZ 


6     5 


^ 


XE 


^ 

-', 

'V 

/J 

^^    ^       1 

'■^  --«- 

<* 

— p 

_l 

1 

6       - 
4      3 

Illustration. 


9     8 

6 

4 


^.  pTi,-iT^i|..|jT^-'^^ 


-€>- 


TT 


fe^ 


zz: 


H 


JCE 


-^ 


xi: 


9   8       8     7 
6   - 
4  - 


6       9    8        6     5 


8    7 


Exercises. 


f. 


jCE 


2=^ 


XE 


XE 


3      6       6- 
5   4 
2. 


4  - 


8  7 


S 


XE 


"J  g  r  ^  ^ 


^ 


^       46       67         67986 
3  5 

3.   open  position. 


T8 


87 


3  5  4  7  3      6^f 


S 


4.    close  position. 


6-  87  XF 
5  4 


3 


5. 


7  6       ^^ — 


^ 
^ 

m 


5  6 


x> — 

5   -* 


8  7 


*: 


IE 


^ 


Xf — 

3   7 


8        6 


9   8 


T 


"Or 


721 


i 


i 


^i^ 


XE 


V y 

4- 


7. 


6  - 
4  - 


1 

3 


9  8     98 


f 


XE 


^=3 


22 


XE 


3     '6 


6    -    Ji-    6 
5    4       2 


7t 


6     6 
5 


6 
4     7 

it 


42 


PARKHURSr  HARMONY. 
Sight-reading. 


Open  position. 


xc 


§ 


77— P 


i 


XE 


8^  ^6 
2.         4 


1     ^ 


^^ 


S 


^ 


22 


3. 


V 


1 


•o- 


f 


jCE 


8  7 


s 


^ 


^ 


73 <9- 


XH 


3 


2 


6 


Suspension  of  the  Fourth. 
Fundamental  position. 


I 


XE 


JT 


f^r "  -r"  r 


^ 


3cs: 


5  - 
4   » 


m 


XE 


5    - 
♦     3' 


The  full  figuring  of  this  suspension  with  its  resolution  is 
usually  abbreviated  to  4  3. 

It  is  usually  better  not  to  have  this  suspension  and  its  resolving 
tone  (even  an  octave  distant)  heard  simultaneously. 


U 


«>--o- 


^¥r 


9ZXE: 


6      4   8 
5 


But  when  there  is  a  whole  tone,  instead  of  a  half  tone,  between 
the  degrees  of  the  scale  on  which  the  suspension  and  its  resolution 
occur  (so  that  the  fourth  and  third  of  the  chord  arc  in  a  less  harsh 
relation  to  each  other), 


CHAPTER  XIII. 


143 


I 


^J  J II  ^^J  J 


-&- 


^^ 


XE 


bad. 


4    3 


~ry 


4   3 


and  when,  in  addition,  there  is  an  evident  melodic  progression  in 
two  voices,  in  contrary  motion,  such  an  effect  is  admissible,  thus : 


^^ 


i 


Illustration. 


^^ 


-O- 


31: 


xn 


-€> 


XJ^ 


#=t3 


^ 


§ 


1©-    <^ 


-<^^ — "y 


fe-W^t^ 


ax 


-3 O" 


i 


4     8       6    « 
5 


-€>- 


Exercises. 


4    3  7 


xs: 


TT— r!g 


XE 


XE 


30: 


2. 


43      98       43      9  8      4 .3      98        S^bI? 

3 


^S 


i 


nzz^^zsi 


^=jd 


^—d 


4  3      6    6 


3. 


-      6   6      6-    XT 
.5^     437 


ill,  a    <P 


i 


^ 


IX 


zx 


IX 


>  'o 


"^   'O 


3    436436     987     6  51)6         -6     J36     667" 
4.   open  position 


m 


i 


XX 


«tzs 


XX 


XX 


-e>- 


5         4  3       2     6  n  \      %'^        4  3       9  8 


8  7 


XX 


5.    close  position; in  score. 


144 


PARKHURST  HARMONY, 

Sight-reading. 


1. 


o#p|r^llPr;^ 


w 


1SW9 


ISZI^ 


7  6  7 


^ 


f 


«^=^=*5=^ 


^^p 


^c-zz 


-€>- 


ki5 


T^ 


6^ — 7      3  5it> 

4      t 


g 


XE 


riifjij 


i 


^=0: 


O"  76    «  5  '     I 

3  4  3- 

First  Inversion. 


6-flr 


1  ^i 


7  6    <I3" 

4   •«• 

87 


I 


38: 


i 


XE 


r-^r  "M'°r 


^ 


f 


BOr 


5 J—W 


3X 


6      - 
3      - 


Illustration. 


f 


3X 


3      ' 


■iiMH 


r\^J   \'L^    I  i^   C 


P 


«^ 


-0€V 


3CE 


XT 


r^ 


^ 


fS* TT 


I 


3X 


6    - 
3    - 


-€»- 


"sr-g" 


Exercises. 


» 


7      6      1 


5     87     '       7      4  3  7      ^ 


*5     ?r"& 

6  - 
2  3- 


Xfl 


6        I    8      6 


3    H6        6     '7       '6 — » — .6   1,7        9  8      '7    ^ 


5 


7     67 


^ 


^^ 


-^ 


^ 


XI=I^ 


XE 


E 


4. 


B — 9~8r 

1: 


4 
3 


"grg" 
6  - 
3  - 


54^7 


^^ 


-6^ 


■B^ 


I? 

3  - 


"6^ 
54 


3- 


CHAPTER  XIII. 


.    145 


Second  Inversion. 


i^a 


;=s;cr| 


XE 


zt=^ 


r=f 


i 


i 


7     (^ 
4     - 


7    6 
4    - 


7     « 
4      - 


Illustration. 


^^iJJiMi^!-'r^^ 


*y{t "  I  [^  p 


T-ef-^ 


11 


ii 


jC^ 


sr 


p  p|o-4f-g 

l6     |4       98      ^6  5  8 


7  Il6       7    6      Ig     1*       9    8       '6  5  b  7 
5      3"- 


Exercises. 


^ 


^s^ 


? 


jce 


xn 


ztiz^: 


irw 


7   6  ■    ti6    ^ 
4-4 


T-? 


•TIT 
5 


87     O 


rV^l'l'    r  fM  ° 


n: 


?ff 


3^ 


ir~3r 


H 


5^ 


3X 


Pp 


/7 ^ 


R=? 


=F 


xn 


^6        ^TF- 


4  -       4 
3 


6     8  7 
5      \ 


Chord  of  the  Fourth. 


m 


^ 


■^ 


Suspension  of  the 

Fourth,  first 

inversion. 


y|:   g 


3;^ 


■5      3- 


P 


ix: 


JLC 


4         9     8 
3        6- 
3     - 


Suspension  of  the 

Fourth,  second 

inversion. 


p 


t\i(g    |*> 


3 


7    6 
4    - 


146 


PARKHURST  HARMONY. 

Sight-reading. 


Open  position. 


m 


3a: 


t9 (9 


ICE 


2. 


7  6     8    7 
5 


2       6 


8    7 


^ 


m 


3X 


«>- 


^ 


4^  "65  7 


^^W=i^ 


«■ 


k;5 


4  3 


3. 


m 


^ 


1 


i 


5     6       8   7 


6  5 


87 


Ty 


Suspension  in  the  Bass. 

Thus  far  every  suspension  has  occurred  in  the  three  upper  parts^ 
but  it  can  be  introduced  equally  well  into  the  bass,  provided  the  sus- 
pended tone  be  properly  prepared  and  resolved.  This  affords 
opportunity  for  three  suspensions  in  the  bass,  one  of  which  is  among 
the  most  common  and  effective  of  suspensions,  while  the  other  two 
are  suited  only  to  peculiar  circumstances,  and  rarely  occur.  These 
three  suspensions  are  derived,  like  all  the  foregoing,  from  the  fun- 
damental position  and  two  inversions  of  the  common  chord. 

Suspension  of  the  Second  (in  the  bass.) 


The  first  form  is  harsh,  because  the  suspension  (D)  and  its 
resolving  tone  (C,  an  octave  distant)  are  heard  simultaneously. 
The  second  form  is  better,  doubling  the  third  (E),  instead  of  the 
root  (C).  No  figuring  is  needed  under  the  resolving  note,  as  it  is 
the  root  of  the  common  chord.  The  student  cannot  fail  to 
understand  this  suspension,  if  he  will  compare  it  with  the  progres- 
sion in  the  first  two  chords  given  above.  This  suspension  rarely 
occurs  except  in  a  series  of  suspensions  in  the  bass. 


CHAPTER  XIII . 
Illustration. 


147 


I 


^pi 


§=«=iJ 


r 


?r^ 


^^^^^^s 


m 


jlTr^rr 


an 


i 


^ 


-€>■ 


1^ 

5    4  8  7 


6    4 


^5 


4    3 


Exercises. 


si 


s 


^=H= 


?7~^ 


fczzi 


<v 


3XZ 


^^ 


r"^^ 


4    8 


6  7 


Xir 


g 


ff 


T-F" 


a* 


m 


s 


XE 


6  : 


9.8      7  6 
4  - 


Suspp:nsiox  of  the  Fourth   ix  the  p.ass. 


This  is  very  frequently  used,  doubling  either  the  root  or  the  fifth, 
as  above.  The  third  can  be  doubled  only  when  the  melodic  progres- 
sion absolutely  requires  it,  and  needs  no  additional  figure  to  express 
it.     This  chord  is  called  the  chord  of  the  Hfth-and-second. 


i 


^ 


XE 


« 


w 


tx=±^ 


148 


PARKHURST  HARMONY. 
Illustration. 


-€V 


jO_ZL 


w  ■  ^ 


XE 


XT 


^ 


f? 


:or 


-cv 


^ 


i 


zz: 


m 


"»T 


IE 


9  8 
H  - 
H    - 


A  :d. 


Exercises. 


->* — 

3 


* 


S 


xc 


^ 


-€^ 


8    7 


r^ 


^ 


22 


IT 


« 


-€»- 


5      6 


4    3 


3=^=^ 


6  5 


^ 


1^ 


I 


BE 


*J    I  67     4  8 
4.  open  position. 


6    <i    64  3  4-6-0- 
5         5^ 


4  --<5^ 
7 


m 


^ 


XJr 


56  id   5  '6  5 


-€r»- 


3CE 


-^-^^ 


Z21 


6^-^^^ 


i?= 


2   i     877     4"86 


2      ^ 


Suspension  of  the  Sixth  ix  tiii:  p.ass. 


i 


H 


XE 


XE 


XE 


XE 


XE 


X**j 


XE 


«^ 


XE 


^ 


XE 


XE 


XE 


-€V^ 


a. 


c. 


-«>- 


-o- 


-o^ 


^ 


XE 


I 


-7~Tr 

5  4 
3 


3  4 


This  will  be  a  concordant  or  a  discordant  suspension,  according 
to  the  element  of  the  chord  that  is  doubled.  If  the  fifth  be  doubled, 
as  at  (a),  it  is  discordant,  but  if  the  root  or  third  be  doubled,  as  at 
(b)  and  (c),  it  will  be  concordant.  (We  are  here  speaking,  of 
course,  of  the  root,  third  and  fifth  in  the  resolving  chord,  which  is 
the  ruling  harmony  of  the  measure,  although  it  is  fully  expressed 
only  in  the  last  half  of  the  measure).  This  suspension  seldom  oc- 
curs except  in  a  series,  and  whether  tlic  concordant  or  the  discorfl 


CHAPTER  XIII. 


149 


ant  form  should  be  adopted,  depends  largely  upon  the  melodic  pro- 
gression in  the  other  pars,  thus: 

b. 


i 


xr 


xn 


3X 


g 


m 


Tn 


XE 


« 


^ 


-o- 


XE 


js: 


-€^ 


^ 


vrT^t 


i 


The  above  examples  strikingly  illustrate  how   imperfectly  the 
mere  figuring  expresses  the  true  nature  of  a  chord.     Thus  in  the 

7 

first  example,  the  first  chord  of  the  third  measure  is  figured  s. 

Now  it  is  in  the  nature  of  a  genuine  seventh-chord  for  the  seventh  to 
move  toward  the  bass.  But  in  this  case,  being  a  suspension,  it  is 
plainly  in  the  nature  of  the  bass  to  move  away  from  the  seventh ;  yet 
the  two  chords  have  precisely  the  same  figures.  Again,  in  the  second 
example,  the  first  chord  of  the  third  measure  is  figured  ^,  In  its 
construction  it  is  a  common  chord,  in  its  nature  it  is  plainly  a  sus- 
pension, and  thus  the  (apparently)  seventh-chord  in  the  first  ex- 
ample, and  the  (apparently)  common  chord  in  the  second  example, 
are  in  their  nature  identical! 

In  the  concordant  form  of  this  suspension,  as  the  figuring  is      |, 
it  is  unnecessary  to  express  it,  as  will    be  seen  in  the  following: 


Illustration. 


i 


XJl 


H 


xx: 


XE 


H 


-O- 


xi: 


-^rt- 


xx: 


XE 


^p^ 


Xe 


fe£ 


a 


XE 


f 


XE 


-5—6- 
2 


■3" 


t;7 


When  the  suspension  is  in  the  bass,  its  harmony,  being  the  same 
as  that  of  the  succeeding  bass  note,  may  be  expressed  by  a  diagonal 
dash,  pointing  forward  to  the  following  harmony,  which  is  also  to 
be  its  own,  thus : 


$ 


3: 


XE 


-e»- 

XE 


XT" 


ZXEI 


XE 


XE 


O   1(9 


t 


150 


PARKHURST  HARMONY. 


Exercises. 


1.                 ^ ^x 

J  ^#  r ^ — H f- — P-^ ' — ^- — ' — ^-^'^l 

^ 


<p   rj     -77 


XE 


7~ir 
4 


3 


^    - 


Suspension  of  the 
Second,  in  bass. 


Suspension  of  the 
Fourth,  in  bass. 


¥-S      W-T 


Suspensi<^n  of  the 
Sixth,  in  baSvS. 


m 


^ 


i 


^ 


li-^^-^^ 


H 


-&- 


g 


j5^-n^ 


6      7    6 


It  is  needless  to  remark  that  the  foregoing  and  subsequent  exer- 
cises are  really  marred,  musically  speaking,  by  the  extreme  number 
of  suspensions  contained  in  them.  But  these  exercises  are  primarily 
for  technical  drill,  not  for  musical  effect,  and  at  the  same  time  the 
pupil  is  becoming  more  adept  in  the  use  of  those  fundamental  chords, 
by  the  mixture  of  which  we  obtain  all  our  suspensions.  It  is  also 
to  be  observed  that  the  tie,  by  which  the  suspended  tone  and  its  prep- 
aration are  commonly  connected,  is  not  an  essential  element  of  the 
suspension,  and  the  effect  is  often  much  better  if  the  suspended  tone 
be  struck  again,  thus : 


,  The  normal  proportion  of  concord  and  discord  in  music  requires 
that  in  general  the  suspended  tone  (which  may  ^ilways  be  shorter) 
should  not  be  any  longer  than  its  ''preparation,"  as  in  that  case  the 
discord  would  predominate  over  the  concord.  Yet  the  rule  often 
admits  of  an  exception,  as  is  illustrated  in  the  first  suspension  of  the 
foregoing  example.  In  composition  we  find  frequent  occurrence 
of  the  exception,  and,  especially  in  piano  music,  the  omission  of  the 
tie:  whereas  in  orL-ati  music  tlic  ti^'  i^  more  common.     Let  the  pupil 


CHAPTER  XJII. 


151 


discover  for  himself  why  the  tie  should  be  less  used  in  piano  than 
in  organ  music. 

Sight-reading. 
1. 


'y>  r  f  i-i  ^ 


^m 


W7 


4 


-^Mi-J^ 


-€>- 


-t trr 


22 


xi: 


^r^ 


6    5     1}    - 


T 


^ 


* 


zz: 


3X 


xz: 


5-&-       5  1^5      ll>      5-er     'ff 


4      7 


We  have  now  treated  of  all  the  single  suspensions  possible  in 
the  common  chord  and  its  inversions.     We  have  next  to  consider 

Suspension  in  the  Chord  of  the  Seventh. 

The  most  satisfactory  of  all  suspensions  are  those  in  the  seventh- 
chord,  by  reason  of  the  greater  richness  of  harmony,  which  softens, 
without  effacing,  the  discordance  of  the  suspension. 

All  the  possible  seventh-chord  suspensions  will  be  presented,  but 
briefly;  as  no  new  difficulties  are  involved.  The  dominant-seventh 
chord  will  be  used  in  illustration,  as  the  most  common  and  satis- 
factory. 

(While  all  the  secondary-seventh  chords  are  ''fundamental 
chords",  and  as  such  may  have  their  several  tones  suspended  in  a 
following  chord,  it  will  be  found  that  the  seventh  interval  itself  of 
any  secondary  seventh  chord  (either  in  fundamental  or  inverted 
form),  is  too  harsh  to  admit  of  the  delay  in  its  resolution,  and  cannot 
in  general  be  suspended ;  but  any  other  tone  of  such  a  chord  can  be 
suspended.  On  the  other  hand,  the  seventh  interval  of  a  dominant- 
seventh,  or  of  a  secondary-seventh  "in  dominant-seventh  form", 
can  be  suspended,  thus : 


I 


* 


^ood. 


s 


^ 


£ 


good. 


bad? 


XE 


152 


PARKHURST  HARMONY. 


-€>- 


bad. 


§ 


bad. 


* 


XT 

good. 


i 


xc 


«    - 

5      - 
4      3 


The  harshness  of  any  discord  is  softened  by  quickly  passing  from 
it,  and  the  above  that  are  marked  *'bad"  may  be  allowable  when  the 
notes  are  quarters  or  eighths,  instead  of  halves.  Such  effects  will 
be  considered  later,  under  the  subject  of  auxiliary  tones,  Chap. 
XV. 

Suspension  of  the  Ninth. 

Fundamental  position. 


I 


s 


TfQ- 


H 


&z^ 


xw 


b. 


W 


XE 


33E 


II — w 

7  - 
It  will  be  remembered  that  in  the  seventh-chord  the  root  is  often 
doubled,  and  the  fifth  omitted  (as  above  (a)  ).  This  affords  oppor- 
tunity for  the  suspension  of  the  ninth,  in  connection  with  the  sev- 
enth (as  above  (b)  ).  The  third  can  be  omitted,  instead  of  the 
fifth,  but  this  should  not  be  done  when  it  can  be  avoided. 


First  inversion. 


I 


l^ 


i 


m 


It  will  be  seen  that  this  results  in  a  chord  of  the  seventh  on  B,  and 
being  resolved  similarly,  it  will  be  regarded  as  a  suspension  only 
when  occurrmg  in  a  series. 


Second  inversion. 


I 


s 


m 


CHAPTER  XIII. 


153 


This  results  in  a  first  inversion  of  a  seventh-chord  on  B,  resolves 
similarly,  and  needs  no  special  comment. 


Third  inversion. 


^ 


w 


m 


■? — 3- 

This  results  in  a  second  inversion  of  a  seventh-chord  on  B,  re- 
solves similarly,  and  needs  no  special  comment. 

In  the  above  set  of  suspensions,  the  first,  called  the  chord  of  the 
ninth  and  seventh,  alone  requires  practice. 

Illustration. 


— r — c)     o — A  ^ 


P 


g       I  ^—r,  _CV 


^ 


!z=e 


■*>- 


I 


t 


TH 


-WW 

7    - 


5 


4     3 


9   8 

7  -■ 

i 


Exercises. 


8H7 


m 


t 


8 '; '       " 


Xfl 


s 


^     h  98 

'2.    open  position  q 


4    3 


3ce: 


t 


XE 


1 


XE 


3. 


7  - 


g-B      4    3      9  8 


TP 

9  87 


m. 


XE 


31: 


^ 


9   8      7   6      -(r- 

4    -        5  4 

3 

Suspension  of  the  Eighth. 


■WW 

7   J 


I 


i 


-O- 


^^ 


^ : 


r<>  r "  g  ^^f 


fundamental.         is>  inversion.      2nd  inversion. 


3rd  inversion. 


^ 


XE 


XE 


-o- 


-O- 


5 


154 


PARKHURST  HARMONY. 


The  suspension  of  the  perfect  eighth,  resolving  into  the  seventh, 
presents  again  the  anomaly  of  the  common  chord  in  the  aspect  of  a 
suspension,  and  it  would  certainly  never  be  classed  as  such,  except 
in  such  connection  as  the  following 


i 


mMLlilAiU£ 


nzz 


XI- 


JDL 


«^ 


-€>- 


^ 


xs: 


<^ \^^         i 


xx: 


XE 


where  the  ruling  harmonies  of  the  measures  are  as  follows : 


I 


^ 


«^ 


x^: 


^ 


§ 


5i? 


JCk. 


-€>- 


?ut  by  the  use  of  the  diminished  eighth, 


4>  I      <t 


XT 


I 


W^ 


§ 


i* 


-€>- 


8     7 


we  get  an  unequivocal  suspension  above  the  seventh ;  but  it  is  too 
harsh  for  frequent  use. 

Suspension  of  the  Sixth. 
Fundamental  position. 


m 


xn 


J/'  fi 


XE 


7    - 
ft     5 


In  the  common  chord  this  suspension  lacks  the  discordant  quality, 
which  is  here  furnished  by  the  seventh  (F)  in  its  relation  to  the  sixth 
(E). 


CHAPTER  XIII. 


155 


t'lrst  inversion 


Second  inversion: 


^ 

-p^ 

y  " — 1» — 

6  - 
5  - 
4     8 


>J  J  II  ^JT^J  J 


bad. I 


good. 


«1^ 


1 


tl 


JlX. 


4    - 

8  - 


This  is  not  good  in  four-part  harmony,  but  good  in  five-part. 
Third  inversion : 


I 


-pis-- 


»V  P  I  o 


6       7    6 

4       4    1 

2    - 


Let  the  pupil  indicate  all  the  sixth-suspensions  in  the  following  t 


4|,TlA^J^dJM.^^.'lTd^l:J,^l-ll 


J  » 


xz: 


i  JJ 


i 


«F 


XE 


XE 


XE 


3Ct 


rt 


6   - 

Is 


9  8 


7    - 


7  6 
A-  - 
2    - 


7    6 
6 


156 


m 


PARKHURST  HARMONY. 
Exercises. 


xn 


i 


Xfl 


o^ 


^         6  5 


^^ 


6        9   8      76      W 


^7 


'3      6  4  3      I  I         '6    is-      6    I      ^ 


^ 


3      6 

3-      open  position. 


#     2 


-^ 


6     8  7 


-^- 


3        1^6 

4.  close  position. 


XE 


6  -       4    3 
5 


7  - 
6  5 


^^3 


6        65 
4  3 


^ 


5=31 


fei 


9    8       7 
7   6 


i 


33r 


-C^ 


i 


5. 


6    5       6-       98      li      8  7        <^ 


g 


-^ 


xi: 


-€>- 


id 


3      6       T^     y^      6l6¥  tJ6 
4  -      4   -  (>5        ^ 

2    - 


4      7 


The  pupil  should  examine  each  suspension  in  the  foregoing  and 
subsequent  exercises,  and  give  its  exact  name,  according  to  the 
previously  given  method  (page  137).  Faithful  practice  of  this  sort 
will  give  a  mastery  of  the  subject. 


Sight-reading. 


^ 


<y-77 


m 


zz: 


•        i      6     [" 


XE 


3       7 


Jr      6  -6- 
2 


6      6^ 
4 


s 


rjhirir^i;Mi:,^ 


IE 


5       8  7     8  7 


^I 


^^ 


§ 


55^ 


ES^ 


f-HS^ 


-<v 


3     6         "J 
4.-  ^ 


6        -e 


s  ? 


I  *  ' 


S     4 


CHAPTER  XIII. 

Suspension  of  the  Fourth. 


15? 


Fundamental  position. 


i 


w 


The  above  figures  J  call  for  only  F  and  C.  By  what  author- 
ity is  D  inserted?  The  harmony  of  the  first  half  of  the  measure 
(in  a  suspension)  is  found  from  the  tones  of  the  second  half,  only 
substituting  the  suspended  tone  for  one  element  of  the  chord. "  As 
the  figures  ^  mean  the  seventh-chord  on  G,  it  of  course  involves 
the  £fth  (D),  which  is  therefore  in  the  harmony  of  the  first  half  of 
the  measure. 


First  inversion : 


^^ 


«F 


3: 


6     - 
5     - 


a  harsh  and  unserviceable  suspension. 


Second  inversion 


an  effective  suspension. 


Third  inversion: 


I 


^ 


7    6 

4  - 

5  - 


I 


^ 


TV 


m 


■o- 


4        5   4 
2   2 


158  PARKHURST  HARMONY. 

an  effective  suspension. 

Illustration. 


3 


JUL. 


jOl 


Ai 


*J 


jCJi. 


^ 


f 


m 


f 


Ff 


-o- 


-<^~ 


7  6 
4  - 
3    - 


3    3 


4  3 


'^ 


Exercises. 


m 


i 


ax 


^s 


W 


A^  4     rs  6      6  6      4  3        43-d- 


Ol 


SE 


3     7  6  6      7  6 
4-         4  - 


m 


i 


p 


-o- 


30: 


d     «» 


jCE 


«■ — ^ 


^        4   3 
4 
3.  3 


9  8        7       6 

7  -  5 


4    3 


^ 


i 


XH 


£   'e   ^^    '^.  ^4T^ 


xszzo 


3    6       6 

4 
4.    open  position 


'ti      ^^^ 


6  7 
4 


3 


'>  If  r  ir 

H  8      I?      « 


^ 


XE 


jE 


?  9  8      '7 

5  7-5 

5.    open  position. 


6 

b5 


98       6 
4 


4  37 


■5ar 


^ 


BX 


^6        7^      6 


an 


-^ 


9  8      7   6      -f- 

4    -       5  4 

3  - 


4  # 


^.-, 
^ 


-6- 

^4 
3 


Suspension  in  the  bass. 


Fundamental  position. 


ii^i 


€^^ 


a. 


1 


6     2    7       6        7   7 
6 
3 


\n  o»e  form  (without  doubling  the  root)  equivalent  to  a  chord  of 


CHAPTER  Kill. 


59 


the  second,  as  at  (a).     The  other  form  (b)  is  rarely  serviceable  in 
four-part  harmony. 

First  inversion: 


very  good. 
Second  inversion: 


good. 

Third  inversion: 


m 


-^ 


^ 


vr  rr>f 


6         5    4, 
3    3 


i 


S: 


-o- 


^ 


recognizable  as  a  suspension  only  in  a  series. 

Exercises. 


y   %  rJ  ^ 


331 


Tr 


6  - 
5  4 


^^ 


3    6        5 


& 


7  - 
4  3 


2 


6    -6r     8t!7  6  7 


m 


:kji 


XE 


-^ 


^8 


4   ? 


4 
3 


-jr 


lijO 


PARKHURST  HARMONY, 


4.    open  position. 


m 


n^i  T-^^ 


i 


5.   close,  position. 


6   -6- 


ft  7 


J 


^T--0 


^ 


ff^PTSf 


54  4  3 


9      87 


Summary. 

Necessity  of  auxiliary  chords: — Classification  of  auxiliary 
effects  : — Definition  of  Suspension : — The  characteristic  quality  of  a 
suspension : — Three  sorts  of  suspension : — The  law  of  suspension : — 
What  suspensions  are  possible  in  the  common  chord: — Why  sus- 
pension of  the  sixth  is  more  naturally  regarded  as  a  fundamental 
chord  of  the  sixth: — Suspension  of  ninth  most  efifective  in  which 
voices : — Distinction  between  ninth  and  second : — Suspension  of  sec- 
ond in  tenor : — Figuring  of  suspension  of  ninth,  and  its  resolution : — 
Procedure  in  writing  this  chord : — Suspension  of  ninth  in  first  inver- 
sion, in  two  forms,  and  figuring  of  each : — In  one  of  its  forms  equiv- 
alent to  what  chord : — Suspension  of  ninth  in  second  inversion,  and 
its  figuring: — This  chord  equivalent  to  what  fundamental  chord: — 
Proper  method  of  designating  a  suspension-chord : — What  suspen- 
sions are  to  be  avoided : — Suspension  of  sixth  in  first  Inversion  equiv- 
alent to  what  fundamental  chord : — Suspension  of  sixth  in  second  in- 
version how  figured : — Suspension  of  fourth  how  figured  : — When 
can  its  resolution  (an  octave  distant)  be  heard  simultaneously  with 
the  suspension: — First  inversion  with  resolution  how  figured: — 
Second  inversion  with  resolution  how  figured: — Suspension  of  sec- 
ond in  bass,  in  two  forms: — Suspension  of  fourth  in  bass  how  fig- 
nred : — Suspension  of  sixth  in  bass  in  two  forms  : — In  the  discordant 
form  equivalent  to  what  fundamental  chord: — Tie  not  essential  to 
suspension : — Relative  length  of  preparation  and  suspension  : —  Sus- 
pension in  chord  of  the  seventh : — When  can  a  suspension  be  pre- 
pared by  a  seventh : — Suspension  of  ninth  in  seventh-chord  how  fig- 
ured:— Three  inversions  of  same  equivalent  to  what  fundamental 
chords: — Suspension  of  eighth  (perfect:  and  diminished)  : — Suspen- 
sion of  sixth,  fundamental  and  inverted,  how  figured: — Suspension 
of  fourth,  fundamental  and  inverted,  how  figured: — Suspensions  m 
bass,  in  fundamental  and  inverted  chords,  how  figured. 


CHAPTER  XIV. 


161 


CHAPTER  XIV. 

Suspension   (concluded).     Anticipation.     Syncopation. 

We  have  now  passed  in  review  cz'cry  possible  single  suspension; 
that  is,  in  a  single  voice.  But  it  is  feasible  to  have  suspension  in  more 
than  one  voice  at  a  time,  and  we  proceed  to  show  what  is  possible  in 
this  direction. 

Suspension  in  two  Voices. 

In  the  nature  of  the  case,  the  suspended  voice  moves  after  tiie 
others,  that  is,  alone.  If  two  voices  are  suspended,  they  must  move 
together.  Therefore  any  two  voices,  capable  of  proper  resolution, 
can  be  simultaneously  suspended,  provided  that  they  stand  in  con- 
cordant relation,  so  that  their  progression  into  the  resolution  will 
be  agreeable.     The  following  makes  this  plain : 


c. 


d. 


^^fc^-JiJjiiM 


2±:^ 


Xfl 


«-z: 


fi    WrP  \  rj^o  W  rP  \  rpg^'^l^    ll:£^ 


rf 


jingle,      single.         double. 


bad.       good.    bad. 


§ 


IE 


jSH 


m 


6        9  8     6 4     3 
5  5 


9  8      6       9  8^     98 
43      5       43      ^65 


The  concordant  relation  is  necessary,  because  the  two  suspended 
voices  are  so  conspicuous  in  their  motion ;  as  will  be  seen  in  the 
example,  the  intervals  of  thirds  and  sixths  are  much  more  har- 
monious than  fourths;  and  our  double  suspensions  are  generally 
limited  to  those  in  which  the  interval  is  a  third  or  a  sixth. 

in  thirds: 


^ 


^ 


-3^ 


XE 


iSh-r. 


xx: 


■o^ 


in  sixths : 


F* 

^ — n9 

n rr — 

V      -J 

G ] 

G 

^ 1 

p     |*> 

9 1 

i^ 

r 

i^ 

H 

-j- 

—\ 

o 

«Jfe 

:162 


PARKHURST  HARMONY. 


Double  suspensions,  with  the  interval  of  a  third  or  sixth  between 
the  tones,  are  very  effective  in  the  chord  of  the  seventh,  and  involve 
no  new  principle,  thus : 


M 


U 


*^ 


S: 


i 


:^S 


m 


p^ft 


i'S-rMP-tiKi: 


9-^^ 


•^^77 


TSL 


i-ij 


fe« 


m 


i 


IX 


z::?z 


pT^ 


EXEKCISKS. 


m 


XE 


30E 


-^ 


22 


9  8  9  8  7  6  7  -  9  8 
76  76  4  65  4JJ 
3  -       3  -  4  3 


98 
43 


8  7 


^ 


32 


ft 


fclZ 


-O^ 


I  I 


2     6 


3. 


5  4 
3  3 
2 


XT 

8  7 


^m 


|9— r 


^ 


XE 


-O- 


-O- 


IE 


XH 


3 


9    8     6    !4^       6  l;7     9 
-4.  764      2  4 


9   8      7  -6r    j,7  . 
|6      5  4     ^   a 


^ 


I 


« 


-^ 


¥^ 


XE 


XE 


1 


5.    open  pos 


n  position. 


'  I 


9  8      9     6 
4  U      ^       ^ 


76       7  - 
4  -       6  5 


^ 


^ 


o- 


3CE 


JX 


fczi 


"?      9^     7  6        7  4  -# 

57654       65  >  4 

6.    open  position,    *  ^  3 


^6 


67 


XT 


s 


m 


g     jy 


S 


XE 


6    4        A-    ^^       U-   6 — '6    ^ 
3    3         2  2  3     4 

2  3     3 


81^7      6  7 


Suspension  in  Three  Voices. 
The  usual  method  of  employing  suspension  in  three  voices  will 
be  explained  later.     It  is  of  rare  occurrence,  and  is  illustrated  as 
iollows : 


I    ^Jfe 


m 


XKE 


XT 


CHAPTER  XIV. 


63 


Exercises. 


1. 


& 


-€V 


ics: 


5t|7 


2. 


9  8 

ll4  3 


9» 
7  6 

54 


a7 

4 


9  § 

4  3 


ITT 

4<^ 


9  87 
7   6 


<v 


1 


ST. 


5  -er 


9  8 
7  6 
4  3 


-cv 


XE 


9  8 
6  5 
4    3 


9    8 
4    3 


9  8 
7  6 
3    - 


:n: 


25 


3 


X»" 


#i 


m 


ax: 


■o- 


■€>- 


98 
7  6 
4  3 


9Er 

7  6 
5  4 


7  -6r 
5  4 
3    - 


%} 


9  8 
7  *> 
4    3 


8  7 


XE 


^ 


3cs: 


m 


ii 


3 


6  7 


Resolution  of  the  Suspension  into  Another  Chord. 

Hitherto  the  resolution  has  been  into  the  same  chord,  that  is, 
the  unsuspended  voices  did  not  leave  their  tones  until  the  suspen- 
sion was  resolved.  But  it  is  possible  for  the  unsuspended  voices  also 
to  move  simultaneously  with  the  suspended  voice,  so  that,  while  the 
resolution  is  precisely  the  same  as  before,  the  harmony  of  the  re- 
solving chord  is  quite  different,  thus: 


9  » 


This  can  always  be  done,  provided  the  resolving  tone  is  an  ele- 
ment of  the  new  chord,  and  the  other  progressions  are  correct.  The 
harmony  is  richer  by  this  method,  inasmuch  as  the  effect  of  three 
chords  is  compressed  into  tzvo,  (as  above).  Such  progressions  are 
at  first  more  difficult  for  the  pupil,  and  it  is  indispensable  that  he 
should  clearly  see  the  suspension  in  the  first  chord,  and  its  resolution 
in  the  second.  To  this  end  let  the  following  example  be  carefully 
studied,  in  which  each  suspension  has  several  resolutions. 


164 


PARKHURST  HARMONY. 


§^ 


4th 


9    6 


I 


9th  & 4th  in  bass. 


m^ 


T-jr. 


3^ 


^ 


«-z 


5^-^ 


^ 


^^nci 


^ 


s 


M 


^^ 


^ 


cv 


4    7 


4    -^ 
4 
3 


I  ' 


I  'I 


7  4 
4  3 


6  ^ 
5  4 
4     3 


In  the  same  manner  as  the  resolution  of  the  seventh  is  occasion- 
ally delayed  (chapter  XI),  so  that  of  the  suspension  may  be  delayed, 
by  introducing  a  chord  in  which  the  suspended  tone  is  continued,  but 
becomes  (i)  a  different  suspension,  and  is  then  resolved,  or  (2)  the 
seventh  of  a  fundamental  chord,  and  resolves,  or  (3)  a  concordant 
element  of  a  fundamental  chord. 


S^ 


1. 


i 


1. 


^ 


^^ 


u 


41 


-O- 


IX 


H 


s 


301 


9  4    f 


XE 


4   3 


ry 


-*v 


I  f  If  r  ^^'^ 


2. 


I 


f  tf  ^  I 


*     -S: 


3X 


i 


ff 


i 


3x: 


sh-*' 


I 


4      6 
5 

3. 


^^ 


^1^^^ 
J  i  ^ 


9  % 
4 
3 

[    o 


3: 


i 


XE 


3x: 


CHAPTER  XIV. 


165 


One  way  of  delaying  the  resolution  of  the  seventh  is  by  intro- 
ducing a  chord  in  which  the  seventh  becomes  a  suspension,  and  as 
such  is  resolved. 


This  would  oftener  occur  in  chords  of  the  dominant-seventh  or 
of  dominant-seventh  form,  than  in  the  pure  secondary-sev- 
enth chords.  This  method  of  delaying  the  resolution  of  the  sev- 
enth could  not  be  mentioned  in  Chapter  XI,  as  the  nature  of  sus- 
pension was  not  yet  explained. 

Hitherto  the  resolving  chord  has  afforded  the  true  fundamental 
harmony  involved  in  the  suspension-chord.  But  this  will  not  be  the 
case  when  the  suspension  resolves  into  a  nezv  harmony.  To  de- 
termine the  fundamental  harmony  of  the  suspension-chord,  it  will 
now  be  necessary  to  combine  the  resolving  tone  with  the  other  tones 
heard  simultaneously  with  the  suspension.  In  the  case  of  the  sus- 
pension of  the  ninth,  in  second  inversion,  when  figured  |,  there  will 
be  a  danger  of  misinterpreting  it  as  a  fundamental  chord,  viz.,  the 
first  inversion  of  a  seventh-chord.  As  a  suspension  the  bass  must  he 
doubled;  as  a  seventh-chord  inversion  there  must  he  no  doubling, 
and  the  chord  must  therefore  be  interpreted  and  formed  according 
to  the  requirements  of  the  situation.  But  ^  followed  by  J  com- 
monly means  a  suspension-chord.     In  the  case  of  the  full  figuring 

6    there  can  of  course  be  no  ambiguity. 

Exercises. 


zzz:^ 


s 


^m 


XE 


-<& 


9     7 


5     6 
4 


^ 


g 


XE 


.  i  'J  i  'J 


xs: 


3      6 


6 

^     7 


li 


166 


PARKHURST  HARMONY. 


4. 


m 


^ 


W 


^ 


zz 


6      7 
5 


5. 


6  r  ^ 

^     2       ^ 


9    6     6 
7    4 
3 


6     87 
5 


*>lI>  JIP^ 


i 


* 


zz: 


r^-t^ 


"^i^^W^ 


4      7 

6.      open  position. 


ITT 
5 


6   7 


6    7 


s 


S 


s 


^ 


p 


«HJ^ 


«^-« 


•'4      7 


7.  open  position. 


.9  1,7      » 
l>5 


6    6      4-87 
kl     5      3  - 


^ 


^^FM?. 


^ 


^-z^ 


t 


o  %o 


7       9   4 


17       9 


^6      8  7  6*7 


Delaying  the  resolution. 
8. 


J  f^lffhp 


'J  \Wj  ^  (^ 


t9-^ 


?2: 


9. 


5  '6        9-2645^ 

DO  o 

43  ^ 


4,'6^^ 

2l»5      4  <^ 
3 


6  6^ 

4   ^ 


K      Q  lA   Irr     >nZ^7I        6   '4.   ^     Q    tt  1-7     Q  ft  9.       fi  /  ti.     Q  O  a  V  *-* 


5     9  '6  '7    '6J4-6      6  '4  '7    9   6  1,7    9  8  2      64  6    98  6  7^'^' 
7  4  2  5  '4         43  3        7^54 


10. 


i 


4v..  a;  p  ir^ 


s 


^^M^ 


n: 


zt±^ 


^    98-e-    6 

6-4 
3-  3 


rj  gl  I      g|_L 
-6^     6    9:^ 

^  n7 


11 


5     49l>766       26 
4-5 


xr 


s 


^ 


1 


It  is  an  interesting  exercise  for  the  pupil  to  choose  for  himself 
the  harmony  that  shall  accompany  a  given  suspension.  Thus,  sup- 
posing the  following  notes  represent  the  preparation,  suspension  and 
resolution  in  the  soprano 


I 


^ 


then  the  first  chord  must  contain  D  as  an  element  of  the  harmony, 


CHAPTER  XIV. 


167 


and  the  chord  of  the  next  measure  must  be  such  that  D  and  C 
will  be  a  suspension  and  resolution,  thus: 


^ 


m 


m 


9  S 

We  have  here  a  suspension  of  the  ninth.  By  changing  the 
harmony  we  can  have  a  suspension  of  the  sixth  or  of  the  fourth, 
thus : 


m 


ff 


-€*- 


§ 


^ 


TT 


^ 


4   3 


A  little  practice  will  make  one  quite  adept  in  the  selection  of  proper 
harmonies,  and  make  the  whole  subject  of  suspension  more  clear. 
The  following-  fragments  are  to  be  treated  in  this  way,  letting  the 
given  part  appear  in  tne  soprano,  and  then  transposing  the  parts,  so 
that  the  same  suspension  shall  appear  in  the  alto  and  then  in  the 
tenor;  thus, 


I 


I 


in  soprano. 


in  alto.  in  tenor. 


E 


£ 


^ 


let  the  pupil  adopt  whichever  suspension  occurs  to  him,  and  more 
than  one  if  possible.  It  can  only  be  successful  when  the  pupil  clear- 
ly hears  the  effect  in  his  mind.  The  teacher  can  protract  this  exer- 
cise when  desirable,  and  much  depends  upon  him  to  make  it  interest- 
ing. 

Exercises. 
inc.  L — ^1     I         iL  inG. 


^ 


r^^J    II  t  n,|   J^ 


tlJl'^-"ll'H'' 


^# 


^ 


-^ 


^=jd 


A  variation  from  the  usual  direct  progression  to  the  resolution  is 
that  wherein  tl'-e  suspension-tone  is  shortened,  and  a  harmonic  tone 


168 


PARKHURST  HARMONY. 


(either  below  or  above)  intervenes  between  the  suspension  and  the 
resolution,  thus: 


t^i^i-^Wji^liWlM,    I 


»F= 


g    M>        II IZ 


XE 


i-Jji 


§ 


JOE 


^ 


XH 


^ff 


xn 


f 


XE 


TT 


j|jJ.ii>!7J,^J||JTJj 


b. 


JC& 


T 


§ 


^ 


XJl 


1 


xi: 


xn 


m 


3'     3 


9      8 


6 


6 


This  is  analogous  to  the  movement  of  a  voice  from  the  seventh 
to  another  harmonic  tone  before  resolution.  "Open  position"  is 
more  favorable  for  this  freer  movement  of  the  voice,  as  a  unison  is 
less  likely  to  occur,  and  yet  the  latter  is  not  reprehensible  (as  at  (a) 
and  (b)  ).  The  effectiveness  of  such  a  movement  of  the  voice  must 
be  determined  in  each  individual  case.  When  the  suspension-chord 
resolves  into  another  chord,  the  harmonic  tone  to  be  chosen  belongs, 
of  course,  to  the  suspension-chord.  Harmonize  the  following  in 
half  notes,  and  then  insert  harmonic  notes. 


Exercises. 


i 


m 


ijL_     O     ,      ^ 


m 


n 


XE 


-CV 


6        1*8       7  6    -# 
>.       4-4 

open  position.  3 


7  t> 


«  -  7  - 
54  4  ;i 


1 

m 


-o- 


5? 


-^ 


^ 


7  6     4 
6  3 


8'.   open  position, 


4  -       4   3 


i 


t: 


s 


^ 


i 


m 


4.  close  position. 


9     6 

I? 


87    9 


s 


c»- 


I 


-€^- 


3 


^Te 


5     ^   <J 


4 


xt: 


4  3 


CHAPTER  XIV, 


169 


(2)     Resolution  Upward. 

The  natural  tendency  of  every  discord  is  to  resolve  into  harmony 
by  having  the  upper  tone  lead  downward  one  degree.  This  is  clearly 
the  instinctive  resolution  of  the  seventh,  and  of  every  other  dis- 
sonance brought  to  our  notice  in  "suspension ;"  and  this  still  remains 
the  natural  resolution  of  every  dissonance  even  in  the  present  sec- 
tion, wherein  we  treat  of  resolution  ''from  beneath,"  i.e.,  leading 
vpward.  For  while  the  instinctive  tendency  remains  the  same  as 
before,  to  lead  downward,  when  considering  the  discordant  tone, 
simply  in  and  of  itself,  yet  there  are  other  considerations  which  may 
more  than  counterbalance  that  tendency,  and  require  the  discordant 
tone  to  lead  upward.  These  considerations  are  the  special  require- 
ments of  the  harmony  and  of  the  melody.    For  example, 


I 


^ 


^^ 


■B 


f* 


^ 


^ 


m 


Zr 


3nc 


a  simple  seventh-chord  resolves  as  at  (a),  but  in  a  particular  situa- 
tion, as  at  the  end  of  a  composition,  or  of  one  of  its  sections,  the 
harmonic  sense  will  require  the  resolution  at  (b).  In  this  case  the 
chord  of  C  is  predetermined  by  other  considerations. 

This  ''resolution  upward"  is  frequently  associated  with  "reso- 
lution downward,"  and  affords  the  following  effective  harmony, 
often  found  at  the  close  of  a  composition: 


The  ear  prefers  that  the  suspension  should  lead  up  to  a  tone  that 
completes  the  harmony,  rather  than  dozvn  into  one  that  leaves  the 
harmony  bare,  thus : 


'^      I        good.  bad. 


m 


170 


PARKHURST  HARMONY. 


A  suspension  is  usually  drawn  npzvard  a  semitone,  rather  tham 
dozmtward  a  whole  tone. 


-it 1 -^^— H 

y  ffr %^?^JLL 4 

The  movement  of  a  voice  having  been  estabhshed  in  a  certain 
direction,  a  sort  of  melodic  momentum  will  continue  to  carr}'  the 
voice  in  that  direction,  either  up  or  down . 


^ — g-H^— h^— fo     |o      jo    1I>7Hq      I*%     I^>      |o= 


xn 


^p 


xx: 


m 


XE 


This  often  accounts  for  the  upward  leading  of  the  seventh  in 
the  unusual  progression  of  that  dissonance.     (Exercises  later.) 

(3)     Free  Resolution. 

The  two  foregoing  sorts  of  suspension  are  alike  in  this  respect^ 
that  the  suspended  tone  leads  by  one  degree,  either  up  or  down. 
This  strictness  of  resolution  (by  a  single  degree),  is  sometimes  re- 
laxed, when,  a  movement  in  suspension  having  been  established, 
either  the  exact  repetition  of  a  phrase,  or  else  a  sequence,  calls  the 
suspended  voice  by  a  skip  to  its  original  position  in  the  harmony, 
thus: 


^ 


22 


exact  repetition 


3 


::^ 


P^^ 


11^. 


Sequence. 

The  repetition  of  a  musical  phrase,  at  successively  higher  or 
lower  intervals,  constitutes  a  sequence.  The  phrase  may  be  of  any 
length,  usually  short,  and  either  a  single  part,  or  harmonized  in  any 
number  of  parts,  thus: 


CHAPTER  XI  y. 


\7f 


I 


ZX] 


Xfj 


^►^ 


330 


^ 


J^rnpiPTlrBp^ 


^ 


^^ 


The  several  voices  of  the  harmony  naturally  partake  of  the 
sequence  character.  In  the  practical  use  of  sequence  the  given 
phrase  rarely  occurs  more  than  three  times,  as,  if  more  extended,  it 
becomes  monotonous. 

The  pupil  can  now  understand  the  use  of  "free  resolution"  in  a 
sequence,  thus: 


I 


^ 


€=5 — -a     c 


3 


sks 


W 


-sfe- 


t;:i  ^^^  »|j,y  pppfitp'p^ii^^  rTfC^ri  ^Sg 


Furthermore,  in  the  course  of  "strict  resolution"  an  occasional 
"free  resolution"  can  occur,  when  the  skip  is  made  to  reach  a  tone 
essential  to  good  harmony,  thus: 


a. 


I 


'>-  !  ('  r  Tr  iiJ-f 


b. 


:y  g 


^ 


172 


PARKHURST  HARMONY. 


The  harshness  thereby  resulting,  as  at  (a),  is  skilfully  avoided, 
without  losing  the  force  of  the  suspension,  by  inserting  a  "rest",  as 
at  (b).     This  device  is  of  frequent  occurrence. 

Let  the  following  exercises  be  first  written,  and  then  introduce 
suspension  throughout  the  bass  by  beginning  the  bass  on  the  second 
beat,  thus ; 


I 


± 


-&■    ^ 


^ 


p 


then  let  the  pupil  note  the  examples  of  each  of  the  three  sorts  of 
resolution.  It  will  be  observed  that  the  third  sort  is  of  rare  occur- 
rence as  compared  with  the  others. 


W 


^tt 


mmm\\ny^^ 


2. 


1 


i 


zz: 


i 


xr 


F=^ 


^^ 


3    6 


8. 


8 


4 
3 


m 


^^ 


fW 


36       6     6 


4. 


■6     6 

4     5 


-6r 


S 


iL#ii^);'irJ  Uii^Jj^jMiij 


«>-^ 


5. 


g 


VfVU^VKH^^^^ 


SA-     6-^ 


4    7 


Re-write  these  exercises,  and  put  the  soprano  into  suspension 
throughout.  Such  a  prolonged  series  of  suspensions  would  usually 
occur  either  in  soprano  or  in  bass. 

An  effective  use  of  all  three  sorts  of  suspension  is  found  in 
octave  passages,  where  the  absence  of  harmony  largely  prevents 
dissonance,  thus: 


CHAPTER  XIV. 


173 


le 


m^a 


Figure  the  basses  of  the  following  exercises,  and  analyze 
all  the  suspensions. 


^ — i-j^ 


^^ 


JAA 


-U- 


lA 


rr'r  rr'r  ^^  ^ 


§ 


5=F 


an 


i 


jj^^jjjj|jM^^ 


^ 


f=p 


r    r   TTT 


^ 


jU^J4rii=i=i33ii^ 


rr'r  r  '^-r^ 


f 


i 


*=i=i 


I 


fet 


Lj. 


ft'-r  i|f  8  y*f-f     r'p-p 


^ 


s 


p 


p^ 


2Z 


^-g-f-^ 


-^  ^i  JtJ  J  J 


'ri'''  T  r'irn 


r-TT  ^ 


ifr 


j^ry^f      irfg 


3CE 


Mr  r  ir  f 


174 


PARKHURST  HARMONY. 


i^bfef  i(!  nrm 


XSi. 


PTf 


|n|U|jjjj|j.^li,ijj,^ 


J   JJmJ 


^ 


i 


¥ 


i 


f 


TIT 


rfY''r'rr'rl|''il'^'lfe 


wt  F  ifffyifFf  f^yif'rf  i"ii 


6. 


r 


rmhUf^i^M'fiX/^il^l^j 


pfflff 


i® 


i 


IC3C 


? 


^=p 


In  the  first  measure  of  the  sixth  exercise,  the  third  beat  may 
perplex  the  pupil 


P 


m 


in  deciding  whether  the  figuring  shall  be   7    or   ^,    i.e.,  whether  the 

^  2 

interval  between  bass  and  tenor  shall  be  expressed  by  9  or  by  2.  As 
similar  cases  are  likely  to  occur,  the  distinction  between  a  ninth  and 
a  second  needs  to  be  a  little  more  fully  explained. 

Essentially,  a  ninth  and  a  second  are  alike,  and  ordinarily  all 
intervals  are  reckoned  as  being  within  the  limits  of  an  octave.  In 
the  case  of  every  discord  the  ear  demands  a  compensation  by  having 


CHAPTER  XIV. 


175 


the  two  voices  in  discord  move  into  concordant  relation,  generally 
by  the  upper  or  the  lower  voice  moving  down  one  degree. 


In  the  case  of  a  second,  resolving  into  unison,  there  cannot  be 
said  to  be  a  concordance  compensating  for  the  discord,  as  when  a 
ninth  resolves  into  an  eighth, 


i 


^^ 


U 


I 


2      i 


9    8 


9  8 


and  even  the  latter  hardly  affords  adequate  compensation.  Accord- 
ingl}^  in  such  a  resolution  as  in  the  last  example,  figured  9  8,  more 
than  an  octave  must  intervene  between  the  voices,  that  the  resolution 
may  be  into  an  octave,  and  not  into  unison.  But  where  the  lower 
voice  moves  away  from  the  upper  (as  at  (b)  above),  the  concord- 
ance is  secured  without  the  octave  distance,  and  such  an  interval 
would  be  called  a  second. 


Anticipation. 

The  exact  opposite  of  suspension  occurs,  when  the  voice,  instead 
of  delaying  upon  a  tone  of  the  previous  harmony,  anticipates  its 
tone  in  the  following  harmony,  by  taking  it  before  the  other  voices 
move.  In  Anticipation  as  in  Suspension,  the  voice  thus  moving 
usually  does  so  by  a  single  degree,  up  or  down,  and  rarely  by  a 
skip. 

In  the  following  exercises  let  the  anticipation  be  introduced  in 
three  ways  ;  ist,  in  bass  ;  2d,  in  soprano ;  3rd,  in  the  three  upper  parts 
simultaneously,  each  exercise  being  first  simply  harmonized.  The 
first  four  measures  of  the  first  exercise  are  here  given  in  all  the  ways, 
as  illustration. 


176 


PARKHURST  HARMONY, 
a. 


pil\ii\llf\f]!ti  .iliir^  f  l|-:(g 


anticipation  in  bass. 


nticipation  in  soprano. 


^ 


f    ir  r 


rJ       \?i 


rJ         J      ^ 


\UMJaL  i  fif 


'ZTh   P      0^=^ 


^ 


anticipation  in  sop. alto  and  tenor. 


^ 


m 


f    ir   I- 


Exercises. 


g 


c: 


S        ft    1^ 


■g    I  .;  ^   ij  ^niz^^ 


xi: 


'4        6    '6 


t>    6      ?     6 
^        5 


6        6      7 
4 


^ 


0:fl  P 


f  J  \r)r^  If  ^  I JJ  LJ  ^ 

1      ^        i      6       ^     ^        ^^  6       6 


3. 


*  a 


I ' 


I^^ 


22 


*         5 


6  -e- 


y*^  r  r  irr^  li<tp  ir  J 


i 


3CE 


*^      6  -e- 


3    6^ 


5 


^ 


J4J     I  J 


?rr--<^ 


J6^ 


a.   7 


*^     2? 


Anticipation  rarely  occurs  where  the  tones  are  of  long  duration, 
as  the  discordance  would  not  be  endurable.  It  often  appears  in  such 
manner  as  the  following: 


CHAPTER  XIV. 


177 


It  will  be  seen  that  all  cases  of  Suspension  and  Anticipation  are 
reducible  to  simple  normal  harmonic  progressions. 

Syncopation. 

This  is  closely  allied  to  Suspension  and  Anticipation,  yet  can  be 
easily  distinguished.  The  characteristic  element  of  Suspension  and 
Anticipation  is  the  discordance  produced  by  the  mixture  of  elements 
of  two  chords,  in  which  is  involved  the  rhythmical  displacement  of 
the  suspending  or  anticipating  voice,  which  thereby  is  made  to 
strike  on  the  unaccented  parts  of  the  measure,  while  the  other  voices 
strike  on  the  accented  parts. 

The  characteristic  element  of  syncopation  is  the  rhythmical  dis- 
placement, such  as  is  found  in  suspension,  but  usually  without  the 
discordance  that  comes  from  a  mixture  of  chords.  A  common 
instance  of  syncopation  is  that  wherein  a  single  voice  reiterates  the 
same  tone,  common  to  several  successive  chords,  but  striking  on  the 
unaccented  beats;  thus,  in  the  tenor: 


^ 


P 


^ 


As  an  example  of  syncopation  in  all  the  voices,  the  following 


I 


fe 


r=* 


t5 


^ 


=^ 


appears  thus : 


^i  i^iV 


* 


i 


178 


PARKHURST  HARMONY, 


In  such  cases  the  syncopation  may  also  be  explained  as  cither 
anticipation  or  suspension  in  all  the  voices. 

Sight-reading. 


^^? 


r^tJMf  U'  'Uirji-'f^,io 


4 


2. 


s 


i 


^ 


re   I 


ZE 


ztS 


3. 


.      .^^ 


i 


^5       6    8  7 

It 


«S 


P 


,'r-^'^";;'r 


T^ 


Summary. 

When  suspension  can  occur  in  two  voices: — Why  concordant 
relation  of  the  two  voices  is  necessary : — The  usual  intervals  between 
two  suspended  voices: — Double  suspensions  effective  in  seventh- 
chords  : — Triple  suspensions  : — Resolution  of  suspension  into  an- 
other chord: — When  possible: — Why  effect  is  richer: — How  reso- 
lution of  suspension  can  be  delayed : — When  thus  delayed,  what  the 
suspended  tone  becomes : — How  resolution  of  a  seventh  may  be  de- 
layed : — In  what  seventh-chords  the  delay  is  most  likely  to  occur : — 
Interpretation  of  the  |  chord: — ^Variation  from  dij-ect  resolution 
of  suspension: — Natural  tendency  of  every  discord: — Three  kinds 
of  resolution: — What  considerations  necessitate  an  occasional  "re- 
s(jlving  upward": — Four  situations  mentioned  where  upward  reso- 
lution is  expected: — Combination  of  upward  and  downward  resolu- 
tion : — Resolution  heretofore  by  one  degree : — Explain  "free  reso- 
lution" : — Define  sequence : — Distinction  between  ninth  and  second : — 
Define  anticipation : — Progression  usually  by  a  single  degree : — Syn- 
copation, as  contrasted  with  suspension  and  anticipation. 


CHAPTER  XV. 
AuxiLiAR  Tones. 

An  auxiliar  tone  is  one  that  is  foreign  to  the  fundamental  har- 
mony in  which  it  occurs,  being  either  prepared,  as  in  Suspension,  or 
entering  freely,  that  is,  without  preparation,  llins: 


CHAPTER  XV. 


179 


f 


r 


^ 


It  is  of  the  latter  sort  that  we  are  now  to  speak.  It  is  evident 
that  every  such  tone  must  stand  in  such  relation  to  the  harmony  in 
which  it  occurs  that,  though  foreign  to  it,  it  shall  not  seriously  dis- 
turb the  harmony;  and  the  auxiliar  tone  must  be  very  subordi- 
nate. These  auxiliar  tones  are  of  several  sorts,  and  may  be  classi- 
fied as  follows : 

1st.     Those  "icJu'cIi  fill  out  the  Interval  between  tzvo  harmonic  tones 
in  a)iy  mice,  and  occur  on  tl'.e  unaccented  parts  of  the  measure,  thus: 


This  sort  of  auxiliar  tones  may  be  diatonic,  as  above,  or  chromatic  , 
thus : 


i^^ 


m 


These  chromatic  tones,  however,  may  often  be  regarded  as  strictly 
harmonic,  as  in  the  above  example ;  but  in  many  cases  they  are 
purely  auxiliar. 

Such  towes,  filling  up  the  spaces  between  the  harmonic  tones,  are 
called  passing  tones,  and  are  the  most  frequent  of  all  auxiliar  tones. 
They  are  also  the  least  conspicuous,  because  they  occur  on  the  un- 
accented parts  of  the  measure.  Being  the  least  conspicuous,  from 
their  unaccented  position,  and  their  diatonic  (or  chromatic)  pro- 
gression, they  sometimes  occur  in  a  half-note  movement,  but  usually 
in  more  rapid  tempo : 


180 


I 


PARKHURST  HARMONY. 


rf 


s 


s=±§ 


± 


*>'„  wiUfv^^^ 


It  will  be  readily  seen  that  such  an  auxiliar  tone  cannot  be  used 
as  the  preparation  of  a  suspension,  thus ; 


^ 


IE 


^r*        c>      -^> 


ax 


«IP^ 


■^ 


o- 


ff 


and  it  may  be  said,  in  general,  that  the  preparation  of  a  suspension 

must  he  a  fundamental-harmonic  tone. 

More  noticeable  are  auxiliar  tones  of  the  next  class : 

2d.     Those  which  occur  diatonically  (sometimes  chromatic-ally) 

on  the  accented  parts  of  the  measure,  and  simultaneously  with  the 

harmonic  tones,  thus : 


ir|jJJJ|3.i1 


tj  J  iii^.  ^  '1 


Ff 


m 


s 


Still  more  conspicuous  are 

3rd.  Those  which  appear  by  a  leap,  0)i  the  unaccented  part  of 
the  measure;  in  which  case  they  must  move  by  a  degree  up  or  down 
to  a  harmonic  tone,  thus : 


^% 


n 


^^ 


T 


3X 


W 


-«»- 


■o^ 


¥ 


JCE. 


XE 


XE 


i 


xs: 


^ 


The  abrupt  effect  of  these  tones  entering  by  a  leap  must  be  coun- 
terbalanced by  a  shorter  duration  of  the  tone. 


CHAP  J  IR  XV. 


tdi 


And  the  last  class  of  auxiliar  tones  are 

4th.     Those  which  appear  by  a  leap  on  the  accented  parts  of  the 

measure,  thus : 


lVr^lT^i;r^^^ 


I 


xx: 


sx: 


? 


XE 


In  this  case,  when  the  auxihar  tone  is  below  the  harmonic  tone, 
it  is  better  to  be  distant  only  a  minor  second,  using  an  accidental  if 
necessary  ;  when  above  the  harmonic  tone,  it  can  be  at  an  interval 
of  either  a  minor  or  a  major  second,  according  to  the  location  in  the 
scale.  This  is  because  a  dissonance  naturally  leads  downward,  and 
if  it  is  to  lead  upward,  it  will  do  so  more  easily  if  its  motion  is  only  a 
semitone. 

The  foregoing  classification  of  auxiliar  tones  will  be  easily  re- 
membered when  stated  thus : 

(i)     unaccented,  diatonic  or  chromatic 

(2)  accented,  *'         "'  " 

(3)  unaccented,  by  a  leap 

(4)  accented         '*  ''     " 

and  successively  more  conspicuous  in  this  order. 

Such  auxiliar  tones  as  are  marked  x  in  the  following  example 
may  be  called  auxiliars  of  the  ist  class,  but  they  are  not,  strictly 
speaking,  passing  tones,  as  the  harmonic  tones  between  which  they 
stand  are  identical : 


£jT]  s^nv  I  ^7T]  P 


an 


f 


r 


« 


i 


jCE 


XE 


Still,  being  diatonic  and  unaccented,  they  belong  properly  to  the 
1st  class. 

Let  the  pupil  assign  each  of  the  following  auxiliar  tones  to  the 
proper  class.    The  notes  not  marked  are  all  harmonic  notes. 


182 


PARKHURST  HARMONY. 


1 


X  X 


X         X 


#V^  f._.^ 


f 


^ 


i 


^r^i^^'P^^ 


m 


^ 


As  a  rule,  the  auxiliar  tone  leads  at  once  to  the  harmonic  tone; 
but  two  auxiliar  tones  can  be  used  together  zi'lien  both  lead  naturally 
to  the  same  harmonic  tone,  thus: 


I 


s« 


T 


ffi 


3 


X      X 


^ 


m 


-o- 


An  auxiliar  tone  can  be  inserted  between  a  suspension  and  its 
resolution,  similarly  to  a  harmonic  tone  (see  page  iio),  when  the 
auxiliar  tone  leads  diatonicaUy  to  the  resolution: 


i^ 


^  iTe-^ll^fl'^^J^^^f^^^ 


■i^  -9- 


ix 


a 


m 


3Sl 


m 


n: 


Also  an  auxiliar  and  a  harmonic  toiu  can  be  conjointly  inserted 
before  the  resolution,  or  even  two  auxiliar  with  the  harmonic  tone, 
when  necessary  in  order  to  reach  the  resolution  diatonically : 


r 


CHAPTER  XV. 


.183 


P 


^^ 


^-8 H^,^^^ 


ff^ 


^±8i: 


^-J    ijii^Jji 


B 


TSr  42. 


m 


^m 


p 


XXE 


f 


ixe: 


ST 


When  two  voices  move  diatonically  in  sixths  or  thirds  as  follows, 


^ 


f  f  F  If  J 


a 


XE 


^ 


JDL 


^ 


XE 


xs: 


XJr 


it  is  a  simple  case  of  "passing  tones"  in  each  voice.  But  as  an  in- 
strumental effect,  a  single  part  or  instrument  may  take  all  the  above 
tones,  thus, 


I 


^^ 


rfTjjjjji 


^S- 


xr 


TT]  JTTlj 


J    i> 


^ 


in  which  not  the  adjacent  but  the  alternate  tones  are  thought  of,  in 
their  relation  to  each  other.  It  is  a  double  melodic  progression,  and 
such  a  part  may  be  called  a  compound  part. 

In  the  several  cases  before  mentioned,  the  foreign  tone  was  one 
degree  distant  from  the  harmonic  tone  that  followed  it.  A  less 
frequent  use  of  the  foreign  tone  is  that  in  which  it  is  one  degree 


184 


PARKHURST  HARMONY, 


distant  from  the  harmonic  tone  that  precedes,  and  is  followed  by  a 
skip  to  another  liarmonic  tone,  thus: 


i 


i 


J   Mi 


t 


XE 


» 


«^ 


3^ 


^v- 


^ 


3X 


XH 


X         X 


F^m^=i^ 


?V      X       X 


i 


"•J^JTJ] 


^^ 


HgTffM-^ 


rC»- 


xr 


X       X        X       X  XX 


i 


X       X 


J^^Mih 


f>   1> 


Progressions  similar  to  the  last  illustration  (b)  are  not  so  un- 
common. The  close  diatonic  relation  to  the  preceding  harmonic 
or  passing  tone  seems  to  be  the  justification  of  this  sort  of  foreign 
tone.  A  slight  variation  of  the  above  is  where  the  foreign  tone  is 
repeated,  which  sometimes  has  the  effect  of  a  suspension  prepared 
by  a  foreign  tone,  and  is  admissible  only  in  the  more  rapid  move- 
ment of  quarter,  eighth,  or  sixteenth  notes.  It  is  like  a  prolonged 
single  auxiliar,  or  like  two  auxiliar  tones  drifting  to  the  same 
harmonic  tone. 


p 


fefeiS 


xf: 


tt 


-♦*- 


i 


41:    * 


5 


XE 


XE 


f 


I 


f 


^M 


XE 


XE 


i 


CHAPTER  XV. 


185 


Grace  notes  and  Appogiaturas 


^';iYfn-H  p  ^  \ 


as 


i 


i 


are  simply  auxiliar  tones  of  very  short  duration,  used  according  to 
the  previous  rules. 

The  foregoing,  together  with  Anticipation  and  Suspension,  ex- 
plains all  the  varieties  of  foreign  or  auxiliar  tones.  The  following 
exercises  are  designed  to  give  a  practical  acquaintance  with  the  sev- 
eral varieties,  and  are  preceded  by  a  few  special  suggestions. 

In  the  use  of  passing  tones  it  is  better  to  move  away  from  a 
unison  than  into  unison,  thus : 


good 


bad, 


m 


i 


The  reason  seems  to  be  that  the  ear  requires  to  be  compensated 
for  a  discord  between  two  voices  by  a  harmony  of  the  same  voices, 
which  it  fails  to  get   when  the  voices  proceed  to  a  unison. 

Except  in  rapid  movement,  the  harmonic  tone  into  which  an  aux* 
iliar  tone  leads  should  not  be  heard  in  any  other  voice  simultaneously 
with  the  auxiliar  tone,  except  at  an  interval  of  one  or  more  octaves ; 
and  even  then  it  is  not  well  to  have  the  third  in  the  chord  heard  at 
the  same  time  with  the  auxiliar  tone  adjacent,  excepting  when  the 
third  is  in  the  bass,  i.e.,  in  a  chord  of  the  sixth. 


jj„  j|i^  jjj||4.utd 


^ 


bad.  good.     bad.  good. 


:r      ,.     Ilf    f 


a 


i 


p 


301: 


With  a  rapid  movement,  and  especially  with  fuller  harmony  (fre- 
quently in  instrumental  music)   this  prohibition  is  not  enforced. 


186 


PARKhURST  HARMONY 


$ 


8 


^ 


We  are  not  limited  to  single  auxiliar  tones.  They  may  occur  in 
two  or  more  voices,  and  produce  a  great  enrichment  of  the  harmony. 
They  may  be  in  parallel  or  in  contrary  motion,  and  of  the  several 
varieties  of  auxiliar  tones  simultaneously. 


^  p  \>{'  II  (i  i  ^i'  II  p  j*.  -i-^-^ 


in  two  voices. 


£ 


£ 


in  three  voices. 


m 


i 


e 


i4-^  i^r  i  ^  II  ^)   i  IJ"J 


in  four  voices. 


i 


^ 


In  the  above  examples  the  foreign  tones  are  all  "passing  tones." 
It  is  more  usual  to  combine  a  ''passing  tone"  in  one  voice  with  a 
foreign  tone  of  another  variety  in  another  voice,  thus: 


I 


i 


± 


Tm 


i 


f 


9 


Jjiir'tit-f 


J 


4 


S 


f 

The  use  of  "harmonic  tones",  in  which  any  voice  passes  from 
one  tone  of  a  chord  to  another  tone  of  the  same  chord,  either  singly 
or  combined  with  other  harmonic  or  foreign  tones  in  other  voices, 
is  alwavs  admissible,  thus : 


CHAPTER  XV, 


187 


^ 


r^ 


SS=^ 


^^ 


XE 


-O- 


i 


P 


XE 


n 


sy 


rf^^— 'fi'- f '  f  '^ 


g^J^J'Jl^Pj 


XE 


The  combinations  are  endless  which  are  thus  attainable  by  the 
use  of  harmonic  and  auxiliar  tones.  The  simplest  flow  of  harmonies 
can  thus  be  amplified  into  the  most  elaborate  and  masterly  composi- 
tion, which  will  yet  be  readily  understood  by  the  listener,  because  all 
this  elaborateness  is  as  it  were  merely  a  beautiful  veil  which  only 
half  conceals  the  simple  underlying  harmonies.  Thus  the  above 
examples  rest  upon  the  following  simple  chords: 
a.  .1  b. 


^N 


J 


c. 


^^ 


xc 


XE 


«±# 


^ 


i 


^ 


XH 


^ 


XE 


^^6  16  6        ^'6 

The  {nteUigibility  of  an  elaborate  composition  is  proportional  to 
the  simplicity  of  its  fundamental  harmonies.  This  is  strikingly 
illustrated  in  the  opening  eight  measures  of  the  last  movement  of 
Beethoven's  Sonata  Op.  2y,  No.  2,  the  first  six  measures  containing 
only  three  different  basal  harmonies,  and  all  the  tones  being  "har- 
monic," without  a  single  ''auxiliar." 
Presto  agitato. 


^^^^^^P 


^H^^'^^^H 


^ 


^ 


XE 


m 


186 

mm. 


FARKHURST  HARMONY, 


^ 


^^ 


g^to 


9^  $y 


gff^CT^^^^^i 


^ 


I J  iJii 


I 


M 


s 


^ 


^ 


TCE 


g^ 


3 


SE 


6  x6 

5 

This  matter  of  fundamental  harmonic  simpHcity  will  be  alluded 
to  again  later. 

The  following  exercises  are  first  to  be  harmonized  simply,  as 
heretofore,  and  then  made  more  elaborate  by  the  use  of  auxiliar 
tones.  Let  all  the  exercises  first  be  written  with  only  the  embellish- 
ment of  passing  tones,  in  whatever  voice  eflfective,  and  let  them  also 


CHAPTER  XV. 


189 


h?.  introduced  in  the  bass.  Then  re-write  all  the  exercises,  using  the 
:iuxiliar  tones  of  the  2d,  3d,  and  4th  sorts  wherever  possible,  hut 
only  "where  the  effect  is  made  more  musical  thereby,  and  noticing 
carefully  which  sort  of  auxiliar  tones  is  used  each  time.  Be  careful 
that  the  embellishment  he  not  confined  to  any  one  voice,  but  distrib- 
nted  among  them  all. 

Attention  must  also  be  given  to  the  following : 

Uniformity  in  the  Rhythmical  Movement. 

Every  composition,  and  these  exercises  as  well,  must  have  a  cer- 
tain uniformity  in  the  rythmical  movement.  Thus,  if  the  movement 
be  mainly  in  half  notes,  the  steady  current  of  this  movement  would 
be  much  disturbed  by  having,  now  and  then,  a  whole  measure  filled 
with  eighth  notes,  thus : 


S3L, 


^y^i^A-^ 


-&- 


xe: 


;y>  1,1 1„  |..  1,^1^^^ 


ff 


TF 


There  is  no  regular  flow  in  the  foregoing,  because  the  different 
currents,  in  half,  quarter,  and  eighth  notes,  conflict  with  each  other. 
It  would  be  better  as  follows : 


JQL 


If  the  current  start  in  quarter  notes,  this  movement  must  pre- 
dominate throughout,  with  only  very  occasional  half  or  eighth  notes , 
thus : 


^m 


« 


iiiiji 


^^ 


^ 


jCfc- 


XI. 


PF^F 


i 
^ 


190 


PARKHURST  HARMONY. 


-<t  r).  J 


^_  ^  ,A—rrn 


Xfe- 


^ 


^         \  -r- 


wpsm 


i^r~-i-i  j 


XlL 


-O- 


r 


If  there  be  any  noticeable  change  in  the  rapidity  of  the  move- 
ment it  must  be  from  slower  to  faster,  which  will  give  a  climax  to 
the  movement,  whereas  from  faster  to  slower  will  produce  stagna- 
tion. The  exact  degree  of  needful  uniformity  in  the  movement  can 
never  be  prescribed — it  must  be  felt.  The  foregoing  suggests  the 
essential  points  in  the  matter. 

These  exercises,  faithfully  studied,  will  prove  the  most  interesting 
thus  far,  and  can  be  re-written  several  times  by  altering  the  position 
of  the  upper  voices  through  the  use  of  harmonic  tones.  In  addition 
to  the  writing  of  the  exercises,  the  student  is  earnestly  advised  to 
study  the  work  by  J.  S.  Bach  entitled  ''371  vierstimmige  Choralge- 
sange"  (Breitkopf  and  Hartel)  to  learn  how  harmonic  and  foreign 
tones  are  used  in  strict  four-part  harmony  by  that  greatest  master  of 
the  art. 

Illustration. 


I 


pUffji^^ 


^ 


fFff 


i 


-;)'jyi  If  If  iJ^Lir  |/|ff,  f^=^ 


XX  X    .X 


^^J,j  jj.j,-^Avj 


^^^^^ 


Tf 


jl  rj  u  A^M 


J 


11 


m 


CHAPTER  XV. 


i9l 


9-i       f — Lf-   »f       l-f ^= 


331 


i^^ 


Exercises. 


*>#  f  P 


£ 


sw 


a    ^    *      -e-  6       3     6  6       9  8 


6       -6- 


3,   5 


^^^ 


« 


^ 


3  5-fr     g       I'e 


P^ffr 


'     87         ^ 


6-43  «  8*7 


''"'^'Jyj^"''i,^f^^^ 


6^6  ^      .^     ^ 

4 


5. 


m 


i 


-k^ 


a 


TT 


€^-€f- 


22=03 


,6         B7'6  i,t> 


a       6    87 
4 


6. 


3  6     H    6         1,4    'e    2  7         V6      6, 


^ 


^      'I 


?6      6,6 
4  ts 

o 


^      5  8  7 


7.  open  position 


i 


IE 


KZ 


5  ir     6 

4 
3 


-6- 
4 
3 


-6-    |i 
4 
3 


192  PARKHURST  HARMONY. 

8.   opeir position. 


Mu-w  niM^^m 


M- 


9.    close  position. 


-rf  ''' 


6? 


i-l-p-ni- 


» 


^*S 


^ 


f^eW. 


Wa^    Trie 

3 


7     « 


10. 


M^ 


zc 


■^►— u 


— c^  .\a    I,    11,    c 

5^6        6     -t       6      ■« 


tl5 


7      •?    "7       1^     6 
4 


^ 


^ 


S     5 


9    6 


4    7 


12. 


^ 


j^LdX 


#        5  ^  5 


ix: 


6        67 
4 


m. 


open  position. 


#  ^  47 


14.  close  position. 


S 


^ 


5t      4    >       g 


9      6 


6*6         9865 
4  j» 


The  above  exercises  admit  of  great  variety  in  the  harmonizing, 
so  that  each  can  be  written  in  several  ways.  The  pupil  is  advised  to 
exercise  all  his  ingenuity  in  the  use  of  foreign  and  harmonic  tones  in 
the  different  voices,  with  suspensions,  so  as  to  acquire  a  fluent  use  of 
elaborate  and  yet  natural  harmonies.  If  further  exercises  are  de- 
sired, the  pupil  can  make  use  of  any  of  the  basses  previously  given 
in  this  work.  Open  position  will  be  found  far  more  favorable  for 
the  free  movement  of  the  inner  voices,  and  the  judicious  alternation 
of  close  and  open  position  will  secure  the  most  satisfactory  musical 
results. 


CHAPTER  XV. 


193 


Sight-reading. 


Open  position 


SS 


^7         t> 


^^ 


-«^ 


5    6 


fio 


2. 


m 


22=:^ 


XE 


6      «8T 
5 


3     7 


-6r 

4 
8 


3. 


yir~g 


1 


(9 »5-t5^ 


4»    Ip  r; 

'8  7'     4 


^*- 


va: 


-wy 


5       8  7 


8  7 


^LU-a 


gC|g 


^ 


f 


4  5 


Parallel  Perfect  Fifths. 


The  progression  of  parallel  perfect  fifths,  which  is  invariably 
prohibited  in  fundamental  harmonies,  is  occasionally  admissible 
when  one  or  both  of  the  tones  forming  them  are  auxiliary  and  of 
short  duration,  the  effect  in  such  case  being  so  transient  and  inci- 
dental as  to  be  hardly  appreciable,  while  the  avoidance  of  them  might 
be  at  the  expense  of  a  smooth  and  natural  progression  of  the  voices , 
thus : 


4J^iiWi^ 


|by#¥p 


b. 


Lj4giLJ 


^=^ 


^ 


i 


4     -J. 


m 


\f — ^ 


Summary. 

Auxiliar  tones;  unprepared  auxiliar  tones  classified  into  (i)  un- 
accented diatonic,  (2)  accented  diatonic,  (3)  unaccented  skipping, 
and  (4)  accented  skipping: — Preparation  of  suspension  must  be 
what: — Two  auxiliar  tones  in  succession: — Suspension  followed  by 
auxiliar  tone : — Meaning  of  a  "compound  part" : — An  auxiliar  tone 
having  its  relation  to  a  preceding  harmonic  tone : — Grace  notes  and 
appogiatures : — Moving  from,  not  toward,  a  unison : — An  auxiliar 


194  PARKHURST  HARMONY. 

and  its  following  harmonic  tone  not  to  be  heard  simultaneously: — 
Auxiliars  in  two  or  more  voices : — Harmonic  tones  how  used : — Uni- 
formity of  rhythmical  movement: — Allowable  parallel  perfect  fifths. 

CHAPTER  XVI. 
Rhythm.     Primary,  Sfxoxdary.  and  Auxiliary  Chords. 

Rhythm  is  accentuation  occurring  at  equal  inten'aJs.  Tt  is 
the  pulse  or  beat  of  music.  The  interval  between  any  pulse 
■and  the  next  succeeding  pulse  is  measured  off  by  what  is  termed  in 
music  ''the  measure  ;''  the  pulse  or  beat  occurring  at  the  beginning  of 
each  measure.  The  interval  of  time  between  two  successive  pulses 
may  be  long  or  short,  but  it  must    in  general  be  uniform,  throughout 

the    given    composition.      A    'Svhole    note"  ,    A 

as  its  name  implies,  normally  fills  the  measure,  /jkCj  *-^- 

"i.  e.,  expresses  the  duration  from  one  pulse  or  «/ 

emphasis  to  the  next.  But  the  emphasis,  strictly  speaking,  can  be 
made  apparent  only  by  the  contrast  of  emphasized  and  unemphasized 
tones.     If  two  whole  tones  succeed  each  other, 

A 


i 


the  beginning  of  each  measure  has  an  emphasis,  but  it  can  be  made 
apparent  only  by  intermediate  tones  receiving  no  accent ;  thus, 

A       A 


i 


&-&■ 


There  are  two  generic  sorts  of  rhythm,  the  double  and  the  triple 
rhythm,  according  as  one  or  tzvo  subordinate  beats  occur  between  the 
accents ;  the  first  called  double,  because  every  second  beat  is  ac- 
cented ;  the  other  called  triple,  because  every  third  beat  is  ac- 
cented.   The  following  illustrates  triple  rhythm: 

A  A    , 


i 


^ 


O^^G 


The  varieties  of  double  rhythm  are  expressed  by  the  following" 
figures;  |  (or  t)  \,  \  (or  C)  J,  J. 

The  varieties  of  triple  rhythm  by  the  following  figures ; 

3    3    3    6    9    12    6 

2    4    8    8    8      8    4* 

Compound  rhythm  is  that  wherein  the  double  and  the  triple 
rhythm  are  contained  within  the  same  measure.  Thus  a  passage  in 
8'   ^8  ^^  4    ^^^yt^"*"!  involves  both  the  double  and  the  triple  accent . 


CHAPTER  XVI. 


195 


^^^^^^^ 


^^ 


^ 


? 


If  a  measure  be  filled  by  two  equal  chords  the  first  will  be  ac- 
cented, the  second  unaccented.  By  virtue  of  the  accent,  the  first 
chord  acquires  greater  importance  than  the  second,  and  makes  a 
stronger  impression  upon  the  mind.  This  can  be  illustrated  by  play- 
ing the  following  series  of  accented  and  unaccented  chords,  and  after- 
ward playing  only  the  accented  chords,  which  will  be  found  to  convey 
largely  the  musical  idea  of  the  whole : 


i.^ijifg-;  I  a 'I 


W 


I 


^ 


u 


13 


n: 


<r>^ 


«5^ 


i 


^ 


XE 


■j*      ..     -     --=-^^-^-=— iJ-^--7;      -        g     -     -^-^ 

ij—ii — r     f -(-— ^ — 1 '^-—\ 

The  same  thing  is  true  in  triple  time,  though  less  markedly,  since 
Tjy  playing  only  the  accented  chords,  tivo  are  omitted  for  every  one 
that  is  played. 


J'     a    J        JU.. Y^-r.    J     1   »■     —m-  J  -       J  ,    ^-»-| 

-4»J5-3 1 r— r 1 .i r«— ^iH 

1 2 ^'iJjfJI  o- 1 11 'i       U      1 :i 

The  foregoing  examples  illustrate  the  fact  that  even  fundamental 
harmonies  are  not  equally  important.  As  indicating  the  relative  im- 
portance of  the  accented  and  the  unaccented  fundamental  chords, 
the  former  are  called  the  primary,  the  latter  the  secondary  harmonies 
of  the  measure. 


196 


PARKHURST  HARMONY. 


Passing  Chords. 

The  term  "passing-  chord"  has  no  precise  limits  of  definition.  It 
is  appHed  in  general  to  all  unaccented  chords  in  which  some  or  all  of 
the  voices  move  by  one  degree  (diatonically)  from  one  accented 
chord  to  another. 


The  term  would  also  be  applied  where,  in  a  series  of  passing 
chords,  one  of  the  same  sort  occurs  on  the  accented  part  of  the 
measure;  as  those  marked  "^  in  (c)  and  (d). 

Passing  Chords  are  of  Three  Distinct  Sorts. 

1st.  Fundamental  harmonies,  with  a  regular  progression  as 
such;  illustrated  above  by  all  the  passing  chords  in  (a)  and  (b). 

2d.  Those  in  the  form  of  fundamental  harmonies,  but  zvithout 
the  proper  progression  as  such.  As  in  the  first  measure  of  (c)  and 
(d),  with  the  normal  progression  as  follows: 


^ 


^F|^-^ 


3^ 


^-^ 


proper  progression  of 
chord  of  the  second. 


X 


22 


similar  instance. 


W^ 


^ 


-e>- 


2 


Such  chords,  though  having  the  form  of  fundamental  harmonies, 
have  not  their  force,  but  are  of  the  same  nature  as  Auxiliary  chords 
explained  below. 


CHAPTER  XVL 


97 


3rd.  Aiixiliary  chords  This  term  is  applied  to  all  harmonies  in 
which  one  or  more  voices  contain  unprepared  atixiliar  tones.  (When 
the  auxiliar  tones  are  prepared,  the  chords  are  called  "suspensions.") 
When  the  unprepared  auxiliar  tones  are  also  passing  tones,  there 
result  passmg  chords  of  the  3rd  sort. 

The  three  sorts  of  passing  chords  are  illustrated  thus : 


ffi^i-a-llLU 


*  i-ii-Ui'l'' 


jOl. 


IX 


^ 


fT 


TT 


IX 
first  sort. 


,     second  sort. 


m 


-o- 


xs: 


6   2       6  7 

The  above  choras  of  the  second  and  third  sort  may  be  analyzed 
either  as  auxiliary  passi)ig  chords,  or  as  fundamental  chords  with 
passing  tones. 

Another  sort  of  auxiliary  chord  frequently  used  is  that  in  which 
the  auxiliar  tones  are  not  passing  tones,  but  are  taken  by  a  skip,  as 
already  explained  in  the  chapter  on  auxiliar  tones ;  or  the  two  sorts 
may  be  combined  in  the  same  chord.  Let  the  pupil  closely  examine 
the  following-,  and  determine  the  fundamental  and  auxiliary  chords, 
and  the  different  sort  of  auxiliar  tones. 


_,« . 


Li 


i-A 


^ 


V 


The  Harmonic  Support  of  a  Melody. 

In  the  definitions  of  the  Introduction,  the  distinction  between 
melody  and  harmony  was  shown.  The  two  are  radically  different, 
and  can  be  to  a  considerable  degree  separated  from  each  other,  hut  not 
entirely.  In  a  succession  of  chords  there  may  be  nothing  apparent 
that  seems  worthy  the  name  of  melody,  yet  doubtless  there  cannot 


198 


PARKHURST  HARMONY. 


be  even  the  simplest  succession  of  connected  chords  in  which  the 
experienced  ear  cannot  detect  at  least  a  faint  quality  of  melody, 
either  in  one  part  or  another.  The  utter  divorcement  of  melody  from 
harmony  seems  impossible.  But  how  is  it  when  a  melody  is  per- 
formed which  is  absolutely  free  from  all  harmonic  accompaniment? 
Do  we  then  have  melody  alone,  pure  and  simple?  No,  for  in  such 
case  the  melody  is  the  audible  edge  of  an  inaudible  harmony. 
Melody  is  linked  into  harmony,  and,  in  its  performance,  drags  the 
harmony  more  or  less  distinctly  through  the  mind.  When  a  well 
known  melody  whose  harmony  is  familiar  is  performed,  the  associ- 
ated harmony  is  quite  clear  in  the  mind  of  the  hearer.  In  a  melodic 
passage  like  the  following, 


I 


^^ 


XE 


the  intelligent  musician  will  find  that  he  is  accompanying  the  melody 
with  a  delicate,  filmy,  harmonic  support,  like  this,  for  example : 


i 


J  J  J  j  ij  J  J  Js^ 


3X 


-^ 


3x: 


^ 


XE 


XE 


XE 


There  are  four  ways  of  determining  such  unexpressed  attend- 
ant harmonies : 

I  St.  By  the  tones  of  the  melody  itself,  when  they  are  all,  or 
nearly  all,  elements  of  the  underlying  harmony,  thus : 


i^^ 


^ 


0         0 


4)1      _  I  [o  I 

-^ — —L.^ 1 J 


rriri[j:£;JiTiTj 


^ 


t 


m 


X 

i 


XE 


CHAPTER  XVI. 


199 


2(1.  By  the  metrical  recjnirenients  of  a  composition  when  de- 
manding the  cadence-formula  (see  Chap.  XTX.).,  as  at  the  end  of  a 
composition   (as  in  last  measure  at  x). 

3rd.  By  the  last  expressed  harmony,  when  the  tones  of  the  mel- 
ody are  not  conspicuously  foreign  to  it,  thus : 


^ 


r:\ 


]7TJ^ 


/C\ 


^ 


J 


i 


■5i 


W=^ 


g 


*~« 


/C\ 


m     «> 


^ 


(This  shows  how  the  same  melodic  passage  may  rest  on  entirely 
different  harmonies). 

4th.  By  the  laics  of  natural  selection,  according  to  which  the 
melody  will  be  supported  at  the  most  important  points  by  the  prim- 
ary chords  ;  elsewhere,  by  harmonies  that  are  simple  and  closely  con- 
nected, thus : 


m 


m 


m 


W¥ 


m 


^ 


^ 


5X 


p 


xt 


rr 


g 


^ 


^= 


~rT 


H 


-O- 


icr 


n 


i> 


XT 


^ 


-€>■ 


rs: 


XE 


3CE 


I 


IV 


In  analysis,  the  ist  and  3rd  methods  will  cover  most  of 
the  cases  of  unharmonized  melody.  Octave  passages  are  seldom  so 
prolonged  as  to  require  more  than  two  or  three  unexpressed  har- 
monies. 

An  isolated  note  is  either  a  harmonic  or  an  auxiliar  note,  accord- 
ing to  circumstaT'ces,  thus : 


tf=FH 


I 


3X 


-O- 


harmonic.  auxiliary. 


m 


JOE 
XE 


i 


200 


PARKHURST  HARMONY. 
Defective  Harmonies. 


Not  infrequently  one  or  two  elements  of  the  chord  are  unex~ 
pressed,  as  in  duet  and  trio  passages,  where  the  circumstances  of  the 
case  must  determine  the  full  harmony. 


m 


b.' 


«z=a 


z 


C? • — KT 

tenor  omitted. 


'y-H'  J  \p 


^? 


TW 


IDC 


-«*- 


'••^'r':i|JJLiiV.^ 


-o- 


^s 


alto  omitted. I     . 


M 


& 


M 


#ii 


& 


(The  voice  omitted  in  (a)  and  (c)  is  supplied  in  (b)  and  (d). 
The  harmonic  analysis  of  duets  and  trios  will   show  that  the 
omitted  parts  are  expressed  in  the  accompaniment. 

In  the  first  of  the  following  exercises  a  single  voice  is  omitted, 
and  in  the  later  ones,  two  voices.  They  afford  opportunity  for  the 
exercise  of  all  that  has  been  thus  far  learned  in  Harmony,  and  de- 
mand careful  study.  Let  them  first  be  filled  out  so  that  the  har- 
monies shall  be  the  "fundamental  chords",  and  afterward  let  the 
added  parts  and  also  the  original  parts  be  moderately  embellished 
with  suspensions,  passing  tones,  etc.  Each  exercise  will  admit  of 
more  or  less  variety  in  fundamental  harmonies  and  embellishment, 
and  the  pupil  is  advised  to  write  each  one  in  as  many  different  ways 
as  possible,  using  ''open"  and  ''close"  position  in  each  exercise,  and 
alternating  as  the  case  requires. 


Exercises  in  Defective  Harmonies. 

If  the  following  exercises  prove  too  difficult  for  the  pupil,  let 
thein  be  reserved  for  the  "review"  (see  page  251). 

After  completing  the  harmony  in  each  exercise,  let  the  chords  be 
analvzed 


CHAPTER  XVI. 


201 


1.    supply  tenor  in  1-3, 


* 


^ 


m 


Z2==«CIS 


f 


9-9^ 


Tt^ 


■■wT  \U' 


^m 


rr'r^r'rrir 


2. 


jn'f-MJ.iNJia 


fi>    g     '   fi) 


iS 


TT 


^ 


r '  r^i'  ir^J|°<^r  Ir  ^1^^  l^ 


8. 


■]  ,1  ij  J  ij 


i 


Hr  ip  T- 


331 


^=T= 


xr 


>L    It ^ r 5 1 ] 

m' <>    \%  '^A-t^  lo^  'i^^  14^  '  ^>  ^ 

.fc^;^ 1 1 

^•''"        'l-r''        '°         '"         '^         '"" 

I 


^ji    supply  alto  in  4-6 


^ 


^ 


<5^-^d ^ 


iJi^ii^^     .^-=^.^i.Jj 


^>^g"         |»        |o         \['     P\r 


xi_ 


^ 


xn 


-€>- 


i 


°-  I  J  ,J  I  J 


J^r^i  1^-^  iJfe^^^ 


rJ   ^     1  CE 


^^ 


^M 


^ 


^4t^ 


^^ 


-c^ 


33: 


X5~ 


202 


PARKHURST  HARMONY. 


6. 


lMt±±AaU 


-J  I J  -I  'I  [ 


-O- 


W 


A 


^^ 


^   ,,]  J   ^   .^^ 


i 


XE 


fTT 


XE 


lij|t|^J    ^h^    H    J    ^    |.)    J 


<© ^ 


XE 


g^ 


^i 


i 


« 


^    ^^iJ  J 


-*>- 


M  r  f    r-i^ 


i 


7.    supply  soprano  in  7-9. 


^ 


rr^^ 


-o- 


'ii  ji  yj 


^^ 


1 


Ff?3fT^EpF?f3f 


pzi:& 


xn 


i 


rifM"  li^r  r 


<f  ix: 


<v 


^-ji,-^  J^i^.-r  ,V,o.j 


fY=^ 


^PF^=gf 


gn~g-B 


^^ 


-♦^ 


f 


9. 


a 


^nr  r\\  \'\f  riT  f  ^ri"^ 


^^ 


r^  I  9—^1  -Dp  I  °p-g-i-'j        I      — I  ^  d 


H 


^ 


10.  supply  bass  in  10-1.2. 


a 


g:  fitfor-'  bks«g 


?2= 


^g 


CHAPTER  XVI. 


203 


4rj,iT^-ii^ii-iJt^jfViV'jLj 


.c>K       iO-       #^e- 


-€>- 


J^^KJ    ^ 


m 


12. 


j<rT>Jj^^j^l"-    |o  JMM^ 


^ 


<v 


*>: .  1.  a 


X»^ 


J3L 


^ 


13.    supply  alto  and  tenor  in  13  -18. 


supply 


hr^jyylyU^ 


fe?^ 


j^ii  o      rj 


^^-  ^    # 


^ 


1X< 


^^ 


f 


r 


14 


1  ^a  .J   ,- 

!    1    1 

-h- 

1     J    J     J     \ 

'   *  i— 

— 5^ 

/J 

^;^- 

*     ^    ^ ] 

1-^   ^^    o 

— P ' 

Le. 

-t— 

r     ^ 

l^^  ''^  ^  |j-i-^  r^-^^j|j- 


332 


P 


? 


izz-r-w 


-j^-P-^f^  p'  f  r  ^f 


lo. 


r 


xr: 


P 


Jl.!-ilJJJj|J^I''^ki  •'^IJJ 


^''■''(-  IrJf'r 


]g-1^ 


# 


p^ 


^",JJ,jJJ,J-^JyJJj|-;jj|jJg^J^JJjj 


^^-i^  irrr  irrrrir .  VMfffrir 


^2= 


204 


PARKHURST  HARMONY. 


17. 


i 


y — q 


^ 


J|J  .M  1^  -M^ 


s 


1^ 


^ 


sac 


300 


r  r  V  r   r 


^ 


18, 


I    JJJ|,UJ  J I  J.  JM^M^ 


?>'"j,rfi'  I'  irrrfrrr  ^  u    ,,  i 


>  -'■  i'ljji.i.j,]  ijjjj 


m   I  g 


^ 


I 


^rrr  r   TN'  'f  r  r 


19.  supply  soprano  and  tenor  in  19-20. 


^ 


N-^-H'-^H^fVf-'rrrVrr  rr 


m 


H^7— ^ 


r'rr  Tj^  ifyi^-i^-^rr^t 


f 


Tj 


.JO. 


^^^^M^i'  f  Vi'^^rA^^'i'r  '-' 


i 


CHAPTER  XV 1. 
21.        supply  alto  and  bass  in  21-22. 


205 


^S.«J  ^J 


^ 


i 


^ 


s 


■g— ?: 


jj^J  jjjjJJU 


JQ_ 


^ 


ifi'i  I  '    'i  '  M  IJ^JJJ 


O- 


Xi_ 


J^j  ,f,^  ^^   ,1>JJ  jiJ  j 


S 


S 


XE 


22. 

¥''JiJji,i.ii„iji.i,i^^^^ 


TE 


^ 


=U: 


i^^       J^^i    i    J 


^ 


^sr  supply  soprano  and  after. 


^ 


.frif'ri^"i-iii',;,i'."il^ 


X3l 


-O 


24. 


ZKX 


^ 


Slow  Progression  of  Fundamental  Chords. 

There  are  limits  in  the  rapidity  with  which  fundamental  chords 
can  follow  each  other,  with  ease  and  satisfaction  to  the  mind.  While 
these  limits  are  not  mathematically  precise,  there  is  a  wonderful  con- 
currence of  opinion  which  forbids  that  the  elementary  chords  should 
follow  each  other,  on  the  one  hand,  too  slowly,  or  on  the  other  hand, 
too  rapidly.  In  the  former  case  the  fundamental  movement  is  too 
monotonous;  in  the  latter  case  the  mind  is  required  to  exert  itself 
unduly  to  grasp  the  movement.  The  normal  tempo  of  the  elementary 
chords  is  one  of  the  requisite  qualities  of  a  successful  performance. 


206 


PARKHURST  HARMONY, 


Ease  of  comprehension  of  a  musical  production  depends  upon  the 
moderate  movement  of  its  fundamental  harmonies,  and  their  natural 
connection.  These  conditions  being  complied  with,  it  matters  little 
how  rapidly  the  individual  tones  and  chords  succeed  each  other. 
Multiplication  of  "harmonic  tones"  or  the  reiteration  of  the  self- 
same harmony  creates  no  new  harmonic  effort  for  the  mind,  and 
auxiliar  tones  and  chords,  in  proper  subordination  to  the  fundamental 
chords,  do  not  obscure  the  transparency  of  the  harmonic  frame- 
work. As  regards  the  multiplication  of  ''harmonic  tones,"  no  better 
illustration  of  this  truth  can  be  given  than  one  that  has  already  been 
-cited,  viz.,  the  opening  measures  of  the  last  movement  of  Beethoven's 
"Moonlight  Sonata"  See  page  187). 

Fine  illustrations  of  a  clear  and  simple  harmonic  basis,  yet  ex- 
hibiting great  elaborateness  by  means  of  harmonic  and  auxiliary 
tones,  is  found  in  J.  S.  Bach's  organ  preludes.  The  use  of  harmonic 
and  auxiliar  tones  in  the  bass,  as  is  so  characteristic  in  Bach,  gives 
an  appearance  of  far  greater  harmonic  complexity  than  really  ex- 
ists. Compare  the  following,  from  one  of  the  above  named  com- 
positions, with  the  subjoined  "harmonic  basis". 


I 


,,  nnnJTn 


h^^ 


h-M^'W^^^ 


S 


f-rf 


i 


CHAPTER  XVl. 


207 


I 


*^ 


^ 


-G^^ 


I 


fa 


S   3*  S>  S»  5^= 


t-i  I  g 


^ 


i 


zi 


p^ 


ai 


^ 


p 


8  iT 


i 


<: 


jmj?Ti^.;^^J7n 


^ 


*  «  * 


S 


? 


*i  0  0 


^ 


f 


* 


i 


w^ 


^ 


j^jJlsm^  ri^iil 


F^ 


f=c 


p r 


s 


^ 


^ 


<r — ^^iP 


208 


PARKHURST  HARMONY, 


No  better  discipline  can  be  found  in  the  analysis  of  harmonic 
structure,  than  writing  out,  in  the  manner  of  the  above,  of  the  funda- 
mental harmonies  of  Bach's  Preludes,  in  which  the  fundamental  and 
the  ornamental  are  so  wonderfully  blended.  Such  an  exercise  as  this 
is  unsurpassed  in  developing  one's  powers  of  legitimate  elaboration 
of  the  simple  chords.  The  limits  of  this  work  forbid  further  illus- 
tration of  this  sort  of  exercise,  or  quotation  of  passages  to  be  an- 
alyzed. The  pupil  needs  to  have  entire  compositions  under  his  hand, 
and  while  Bach's  Preludes  (for  piano  or  for  organ)  are  pre-eminent- 
ly recommended,  the  works  of  any  of  the  classic  composers  can  also 
be  studied  to  great  advantage.  The  contents  of  the  following  chapter 
upon  the  "organ-point"  must  be  understood,  for  the  elucidation  of 
many  passages. 

Such  analysis  as  the  foregoing  reveals  the  fact  that  fundamental 
harmonies  generally  move  no  faster,  often  not  as  fast,  in  "Allegro" 
as  in  "Adagio"  tempo.  The  rapidity  is  gained,  not  by  hurrying  the 
fundamental  chords,  but  by  means  of  the  numerous  harmonic  and 
auxiliar  tones.  Indeed,  there  is  often  a  still  slower  movement  of  the 
foundation  chords,  as  an  oflFset  to  the  brilliancy  of  ornamentation. 

Summary. 
Rhythm: — The  "measure"  : —  Meaning  of  "whole  note"  : — Two  gen- 
eric sorts  of  rhythm  : —  Define  each : —  Varieties  of  double  rhythm : 


CHAPTER  XVII. 


209 


—Varieties  of  triple  rhythm : — Compound  rhythm  : — Passing  chords : 
— Three  distinct  sorts  of  passing  chords : —  Harmonic  support  of  a 
melody: —  Four  ways  of  determining  unexpressed  attendant  har- 
mony:— Slow  progression  of  fundamental  chords. 

CHAPTER  XVn. 

The  Organ-Point. 

The  "Organ-point"  or  "Pedal-note"  presents  the  widest  diver- 
gence from  the  simple  progression  of  fundamental  chords,  and  its 
discussion  has  therefore  been  postponed  to  the  last  chapter  of  har- 
monic construction.  But  this  divergence  does  not  bring  it  out  of  the 
realm  of  lazv  into  the  region  of  license. 

All  tones  heard  simultaneously  must  stand  in  some  consistent  re- 
lationship to  the  fundamental  harmony,  hut  not  necessarily  in  any  re- 
lationship to  each  other. 

The  "Organ-point"  is  an  instance  of  a  more  protracted  use  of 
auxiliary  chords  upon  a  stationary  bass.  The  word  "point,"  in  this 
connection,  is  the  original  term  for  "note,"  and  it  is  called  "organ- 
point"  because  the  organ  is  the  most  serviceable  instrument  for  con- 
tinuing a  tone  indefinitely  without  reiteration.  It  is  also  called 
*'pedal-note"  because  usually  produced  by  one  of  the  organ-pedals, 
while  the  remaining  harmony  is  furnished  either  from  the  organ 
key-board,  or  by  other  instruments  or  voices. 

While  by  the  continuous  flow  of  harmonies  upon  a  stationary 
bass  somewhat  new  and  striking  effects  can  be  produced,  an  an- 
alysis of  the  case  reveals  no  method  of  procedure  that  is  not  de- 
ducible  from  the  previous  requirements  of  chord-connection.  The 
following  is  an  illustration  of  the  use  of  the  organ-point. 


IsF'i'j  i>j.4--tj-u-4^mj 


^F,r- 


m 


h^ 


w 


^m 


m 


^= 


210 


PARKHURST  HARMONY. 


In  order  thoroughly  to  understand  the  development  of  an  organ- 
point,  let  us  take  the  following  example  of  basal  harmonies : 


The  above  are  all  fundamental  harmonies,  except  the  two  chords 
marked  x,  which  are  auxiliary.  If  the  harmonies  at  this  point  had 
been  abbreviated  thus, 


/:'  1J11H1..1 


f 


s 


xf: 


the  auxiliary  chords  would  have  been  in  their  normal  subordinate 
relation  to  the  fundamental  chords,  and  the  A  in  tenor  and  F#  in 
alto  would  appear  plainly  as  passing  tones,  and  D  in  soprano  would 
be  an  anticipation.  Compare  the  original  and  the  abbreviation  care- 
fully, and  the  essential  likeness  at  once  appears.  In  the  original  the 
auxiliary  effects  are,  so  to  speak,  magnified  by  longer  duration.  This 
magnifying  of  auxiliary  chords  is  legitimate  as  a  counterpoise  to  the 
prolonged  assertion  of  the  fundamental  G-chord  zvhich  is  maintained 
by  the  continuance  of  the  pedal-note  through  eight  measures,  so  that 
in  the  aggregate  the  fundamental  and  auxiliary  chords  still  main- 
tain their  normal  relation.  In  other  words,  the  gravitation  of  the 
harmonies,  through  all  the  organ-point,  is  to  the  G-chord,  which 
justifies  what  w^ould  otherwise  be  a  disproportion  of  auxiliary  effects. 
In  the  same  way  other  parts  of  the  organ-point  may  be  embellished 
with  auxiliary  chords  such  as,  in  other  circumstances,  would  be  out 
of  proportion,  as  in  the  following: 


1^  -,-)  iff^i  ^i  >T^  4''  hi  '1 1  - 1  ■■  1  ^ 

>)■  '  1 =i= —  1    1 

1^.       0 Lo Lo — J-o — 0 L^* — Lo  ^  0 ' » 

CHAPTER  XVII. 


21 


Ordinarily  the  chords  marked  x  would  be  expressed  in  quarter  or 
eighth  notes ;  but  whoever  feels  the  magnifying  of  the  entire  effect, 
and  liears  the  G-chord,  sounding  through  it  all,  will  consent  to  the 
prolongation  of  the  auxiliary  chord.  The  above  harmony  can  be 
maintained,  and  yet  made  less  angular  by  the  use  of  passing  and 
harmonic  tones,  thus : 


i 


iC;i.-Jc:>L^t=:;J-L-U 


nrrrfTU^fzrrnf 


«*f 


E 


xn 


It  is  well  understood  that  auxiliary  chords  are  tributary  or  grav- 
itating to  fundamental  chords,  as  seen  in  the  foregoing  illustration 
in  half  notes.  But  in  the  last  illustration  (in  quarter  notes)  we  find 
chords  (marked  x)  which  gravitate  to  the  auxiliary;  these  are  really 
sub-auxiliary  ,  and  this  is  precisely  what  we  should  expect ;  for  when 
auxiliary  chords  are  advanced  to  the  duration  of  fundamental 
chords,  there  would  naturally  spring  up  a  class  of  chords  that  would 
occupy  a  correspondingly  subordinate  position.  We  shall  sometimes 
find  such  sub-auxiliary  chords  in  a  passage  that  would  not  be  called 
an  organ-point,  but  all  such  cases  will  have  more  or  less  of  the 
quality  of  the  "organ-point." 

The  above  can  be  still  furtlier  elaborated,  which  will  increase  the 
auxiliar  and  sub-auxiliar  effects : 


\ll  r  r 

i 

-  If  f  r 

■V" 

— 2 — w — 1 

f — s~ 

f%=— — ^ 

-r^£-f-»- 

^4=. 

H  ' 

-r-#— 

^ 

o    X 

X      )t     X 

X      ^      X 

Lo 

o    X 

Lmmi 

^ 

212 


PARKHURST  HARMONY. 


ox         o  X#X  |»XO*tA         OXX 


^ 


♦i^ 


-^ 


The  above  is  partially  analyzed,  as  follows: 
o  means  fundamental  chord 
X  means  auxiliar  chord, 
#  means  sub-auxiliar  chord. 
The  pupil  should  study  the  above  sufficiently  to  recognize  the 
drift  of  sub-auxiliar  chords  to  auxiliar  chords,  and  of  auxiliar  to 
fundamental  chords. 

This  relation  of  the  different  sorts  of  chords,  and  the  immediate 
and  ultimate  gravitaion  of  all  harmonies,  can  be  exhibited  in  a  tab- 
ular view,  as  follows : 

GRAVITATION 
of  sub-auxiliary  to  auxiliary  chords. 

Hsr^^gi-_      A     I    Jf  r1  J   ■  I    ,       X  <^  X    <^  X  .  X I  X 


mmmms^Y' 


err 

5Ttx    '     ^x  x^x 


m 


r    r  ,ii^jj|j.....^T^ 


I cv 


^ 


^^^^ 


of  auxiliary  to  fundamental  (seventh  and  common)  chords. 


i^ 


fl^fQj^J-^^^Jjj^OfiJS 


XE 


1 


^S 


f 


I 


o  » 


Xfl 


CHAPTER  XVII. 
of  seventh  and  common  chords  to  common  chords. 
><i  X  X 


i 


213 


'-H5 S-r 


XH 


31: 


5^^ 


Z2=Z2 


.X      I    . V  X 


■<^ — u 


3^ 


tS 


JQ- 


r3-!? 


wr 


f 


XE 


30Z 


if  common  chords  (primary  and  secondary)  to  primary  chords. 


'7^=  —  ^--^--'-^''^=^-'^ 

ZU\  [  l^|_|J|_|_L"  J 

of  primary  chords  to  tonic  and  dominant  chords. 


f^ 

F=fl 

^ 

r         r^     P 

^ — 1 

9-      ■ 

< 

9 — 

9—  9-5 — ;  ^ 

O 
X                XX 

o u 

^ — 

^^H — P- h 

1 

li 

of  dominant  cliord  to  tonic  chord. 


^si 


jhatj  Tonic  Chord 


I 


3z: 


« 


The  Ultimate  op 
ALL  Hakmonie*^. 


214 


PARKHURST  HARMONY. 


The  foregoing  table  illustrates  a  very  important  truth  in  Har- 
mony, but  it  must  not  be  misinterpreted.  It  does  not  mean  that  a 
chord  of  any  sort  is  immediately  followed  by  a  chord  of  the  next 
higher  grade.  The  various  grades  are  intermingled  in  countless 
variety ;  but  the  invariable  drift  or  tendency  is  always  from  the  less 
important  to  the  more  important — from  auxiliary  to  fundamental 
— from  seventh  to  common — from  secondary  to  primary — and  among 
the  primary,  the  Dominant  and  Tonic  are  clearly  discernible  as  the 
grand  foci  around  which  the  multitude  of  harmonies  revolve,  like 
"double  stars"  the  centre  of  a  starry  system,  yet  one  of  them  dis- 
coverable at  last  as  attendant  upon  the  other — the  Dominant  upon 
/the  Tonic — and  this  last  the  controlling,  attracting  centre  of  all! 

The  above  "table  of  gravitation"  shows  at  once  which  tones  are 
best  adapted  for  prolonged  use  as  '^organ-points" ;  that  is,  those  tones 
whose  chords  exert  the  most  attractive  influence  through  the  web  of 
harmonies,  and  at  last  assert  themselves,  as  it  were,  in  the  form 
of  a  victorious  "resolving  chord"  after  the  suspense  of  tangled  har- 
monies— the  Dominant  and  Tonic. 

An  apparently  unauthorized  freedom  in  the  movement  of  voices, 
such  as  is  illustrated  in  each  of  the  following  examples  marked 
(a),  is  amply  explained  when  we  notice,  in  the  effect  of  such  pass- 
ages, that  the  chord  is  really  regarded  in  its  entirety,  as  a  compound 
unit,  the  progression  of  the  individual  voices  being  left  out  of  sight, 
and  the  ear  finding  in  the  following  chord  the  harmony  as  a  wJiole, 
which  might  properly  follow  the  discord.  In  such  cases  the  discord- 
ant voice  will  often  fail  to  give  its  resolution,  but  that  resolution 
will  appear  in  some  other  voice,  perhaps  an  octave  or  two  removed. 
That  is  to  say,  the  chord  as  a  whole  is  resolved.  In  the  following  ex- 
amples, compare  (a)  with  (b),  and  the  essential  likeness  of  the  res- 
olution appears.  The  difference  is,  that  the  three  upper  voices  are  in 
a  different  position,  but  the  resolving  chord  is  identical. 


Xfe- 


XE 


331 


«— tf 


m 


J  ^  I  -  ,1 J  J 


« 


XE 


CHAPTER  XV 11. 


215 


This  view  of  the  case  explains  many  progressions,  especially  in 
instrumental  music,  that  appear  quite  lawless.  Thus  in  the  following, 
at  (a)  the  voices  individually  seem  to  move  quite  independently  of 
the  bass,  but  the  actual  chord-progression,  as  a  compound  unit,  is 
the  same  as  at  (b). 


^'mi/Jii'Ji,']!' 


II  'I  r'l  ^'i/'r^'f  n'" 


m 


XH 


^iU^ 


^ 


u 


ft 


As  it  is  natural  to  expect  the  resolution  in  the  voice  that  gives 
the  discordance,  the  mental  effort  in  finding  the  resolution  in  the 
'other  manner,  as  at  (a),  is  too  great  to  admit  of  frequent  occurrence. 
Ytt;  when  the  mind  has  been  aroused  to  a  special  tension,  it  can 
grasp  the  significance  of  a  progression  that  would  ordinarily  be  too 
ibstrlise.' 

The  organ-point  is  most  successfully  prolonged  either  by  the  use 
of  a  sequence  in  the  upper  voices,  or  where  it  underlies  a  melodic 
passage,  already  become  familiar  (as  a  fugue  theme),  thus: 


fe 


rrrryrjj 


^^ 


^F==F 


f 


Fugue  theme. 


S 


-f^f 


i^f 


i^t- 


XE 


The  entrance,  and  usually  the  close,  of  the  organ-point,  takes 
place  at  a  point  of  accent,  and  the  first  and  the  last  chord  must  be 
one  to  which  the  bass  tone  belongs,  thus: 


216 


PARKHURST  HARMONY. 


i—t-f       I'       I  r    f  p 


f 


^^ 


fr=f 


3 


^ 


i 


,JJ^Jjii,j^JJA„l.,    i~i,i  J 


33: 


^1   ^:    ^;   ^G  r.rrr  'r~7 


^ 


^ 


'J  .k  ^^^-   j,j 


^ 


^ 


s 


The  double  organ-point,  on  tonic  and  dominant,  is  possible,  but 
rarely  used,  owing  to  the  occurrence  of  so  many  chords  discordant 
with  either  the  one  or  the  other. 


& 


!JjjiiiJ7fi'i'f'":(^ 


r   rr 


iLLa 


The  dominant  is  far  more  frequently  used  as  an  organ-point, 
as  the  dominant  chord  is  favorable  to  the  continuance  of  the  com- 
position, after  the  close  of  the  organ-point ;  whereas  the  tonic  nat- 
urally leads  no  further,  and  is  best  used  as  organ-point  at  the  con- 
clusion of  a  piece. 

The  sustained  tone,  instead  of  being  in  the  bass,  can  be  in  the 
highest,  or  in  one  of  the  middle  voices,  but  the  other  voices  must 
be  more  constantly  concordant,  as  discordance  in  such  case  is  more 
conspicuous.  As  classical  examples  of  such  sustained  tones  may  be 
cited  the  "Gloria"  of  Cherubim's  Mass  in  C-major,  where  Ab  is  held 
by  the  violins,  while  the  chorus  and  other  instruments  carry  out  their 
several  melodic  and  harmonic  progressions ;  also  the  D  of  the  violins 
in  the  introduction  to  Mendelssohn's  Overture,  "Quiet  Sea  and  Pros- 
perous Journey,"  and  finally,  the  sustained  A,  now  in  the  bass,  and 
now  in  the  upper  and  middle  voices,  in  the  Trio  of  the  Scherzo  of 
Beethoven's  Symphony  in  A-major.  In  all  these  cases  there  are  but 
few  chords  of  which  the  sustained  tone  is  not  an  element. 

To  give  practical  study  in  organ-point  let  the  pupil  elaborate  the 
several  upper  voices  of  the  following  exercises : 


i 


1. 


«: 


S 


CHAPTER  XVII. 


XT. 


XE 


217 


XE 


ICE 


-O- 


33& 


XT 


XJ" 


XT' 


i 


ax 


o^ — «— o — i-^o 


i 


2. 


4l       I    XI 


-^ 


if      O 


3Ei: 


ii     »   «* 


:s^     XT 


_^^ xj: — 5;^ 

XT      ^       :s:      XT 


S 


m 


% 


3. 


Tf Tf 


-*^ 


s 


H     r  «<o  L8 


XKX 


^ 


w 


XE 


^ 


4. 


^ 


_o_ 


XlL 


xj- 


3x: 


«: 


XE 


XE 


XE 


XE 


XE 


XE 


^ 


XT 


^ 


XT 


S 


Summary. 

Meaning  of  the  term  "organ-point",  or  "pedal-note" : — Normal 
relation  of  fundamental  and  auxiliary  chords  in  organ-point : — Why 
auxiliary  chords  can  be  "magnified"  in  organ-point: — Auxiliary 
chords  "tributary"  or  "gravitating"  to  fundamental  chords: — Sub- 
auxiliary  chords,  and  why  permissible  in  organ-point: — The  "grav- 
itation" or  "drift"  of  the  several  sorts  of  chords: — Tones  best  adapt- 
ed for  organ-point : — The  ultimate  gravitating  point  of  all  chords : — 
Apparently  lawless  progression  of  individual  voices  explained  by  res- 
olution of  chord  as  a  whole: — Entrance  and  close  of  organ-point: — 
First  and  last  chord  of  organ-point: — Double  organ-point: — Why 
dominant  is  more  often  used  than  tonic,  as  organ-point : — ^A  sustained 
tone  in  any  other  voice  than  the  bass. 


218  PARKHURST  HARMONY. 

Figure  the  basses  of  the  followiyig  exercises, 
Soi 


% 


^"6   ^W 


^—-(^ 


£ 


m, 


Ok. 


XL 


I 


Alto. 


i 


2  g^ijrj 


nizz 


^ 


ji ^ 


rj  ir^ 


* 


Tenor."^ 


s 


xz: 


21  xf: 


Wf\f'¥V^^ 


Bass. 


^ 


i 


an 


^ 


ZTS3Z 


^^. 


IE 


f^^ 


&-£^£fJjy 


»-77--» 


^^ 


^   (P  |<g 


-^ 


3X 


I 


^Ml^il-Jj|»   -I 


i 


i^ 


-^m- 


±G- 


ZH 


^1  rJlJw^l^y  |f[WJ[4fp("|<t"    J|J 


fjlrjpppi% 


»i:  I  g     1  -e-— ?7 


m. 


^^ 


P 


o: 


ly 


i 


S 


3=^ 


xz: 


^^ 


pg 


I 


fe 


t»'        xg 


it     ^    ,~ 


-^^ 


"Cirr 


I 


i 


3= 


PI"    ^j  |5 


a_.Jf  ^^lt|o 


^ 


m 


z::^c: 


ST. 


g^ 


i 


^^ 


BCE 


^ 


? 


=5^ 


I 


Q  %J^\^J 


rE 


ST^^F^ 


<5^-<p 


^^ 


^ 


<o^ 


i 


i 


^ 


2= 


^ 


zsBzz::^ 


OD(g 


Yf — Wl 


xs 


XT, nCF 


I 


JlpTfTf  f^fffffr 


frflp^^^^M^o  f I "   ^^if 


*> 


*>:.b« 


5 


^i^ 


?^^ 


XXIM 


zz:3t^ 


gl'-'-l-  - 


pj^  fl"  f-^ 


CHAPTER  XVlll. 


219 


M 


XT 


f5^ 


2    "li^^c^ 


^►^ 


Xli 


M 


g 


g 


31: 


JCE 


nr 


^-^ 


I  Hh  [H^ipifiito  rirVf  ii|f  ri4Jr^^ 


S 


#3^ 


-O- 


^ 


^^ 


S22 


-^ 


i 


|€t 


^ 


^S 


^ 


^9G- 


^^ 


I 


^  J4^  J  y 


a 


31: 


^ 


2=^ 


m 


I 


a 


^ 


s 


^ 


^^ 


1^-77 


'iMfhJJlpf'lf' 


zz: 


^ 


^^4fff]fWj 


sg 


ix: 


CHAPTER  XVIII. 
Modulation. 

The  intelligibility  of  a  musical  composition  requires  that  the 
scale  he  evident  in  which  it  is  composed.  A  scale  is  adopted  by  the 
listener,  (unconsciously  indeed)  at  the  beginning  of  the  piece,  and 
the  harmonies  must  so  proceed  that  the  same  scale  is  clearly  main- 
tained, or  that  the  mind,  without  too  much  effort  and  suspense,  shall 
be  able  to  assign  the  harmonies  to  a  new  scale.  The  possibility  of 
maintaining  the  old,  or  of  adopting  a  new  scale,  lies  in  the  pre-em- 
inent significance  and  importance  of  certain  harmonies  of  the  scale. 

By  previous  examination  of  the  several  tones  of  the  scale  it  has 
been  seen  that  they  are  not  a  mere  series  of  tones,  distinguishable 
from  each  other  only  in  pitch,  but  that  they  have  inherent  individu- 
alities in  their  own  quality  or  coloring,  and  are  linked  together  by 
evident  tendencies  of  motion,  which  give  to  the  entire  scale  the  char- 
acter of  an  organism.  The  two  chief  tones  of  the  scale  were  seen  to 
be  the  Tonic  and  the  Dominant,  which  may  be  called  the  focal  points 
of  the  scale.  This  quality  of  Tonic  and  Dominant  is  absolutely 
independent  of  pitch,  and  is  reflected  from  any  tones  that  occupy 
these  respective  positions  in  a  diatonic  scale — reflected  from  them, 
^hen  held  in  a  certain  light,  precisely  as  a  particular  color  gleams 


220 


PARKHURST  HARMONY. 


from  a  diamond  when  turned  to  the  proper  angle.     Thus  the  one 


tone  G 


*: 


b* 


S 


has  the  quality  of  the  Dominant  in  the  key  of  C,  the  quality  of  the 
Tonic  in  the  key  of  G,  and  the  quality  of  the  "leading  tone"  (the 
seventh)  in  the  key  of  Ab.  And  similarly  every  tone  may  thus  be 
made  to  reflect  the  quality  of  every  degree  in  the  scale. 

What  is  true  of  Tonic  and  Dominant,  as  regards  their  importance, 
is  equally  true  of  the  common  chords  founded  upon  them.  They 
are  the  predominant  harmonies  of  the  scale,  occupying  the  significant 
points  in  the  series  of  harmonies,  and  toward  them  the  other  har- 
monies gravitate.  This  is  simply  a  statement  of  facts  in  the  case, 
capable  of  verification  by  the  analysis  of  all  w^ell  composed  music. 
The  pre-eminence  of  the  tonic  and  dominant  harmonies  is  also  plain- 
ly evident  by  their  greater  frequency  than  that  of  any  other  chords 
in  the  scale.  To  become  convinced  of  this  double  pre-eminence,  of 
position  and  of  frequency,  let  the  pupil  analyze  the  first  part  of  dif- 
ferent compositions,  say  fifteen  or  twenty  measures,  or  as  far  as  the 
original  scale  of  the  composition  is  plainly  maintained.  To  illustrate 
the  method  of  analysis  we  will  use  the  first  eight  measures  of  the 
Adagio  of  Beethoven's  piano  Sonata,  Op.  lo.  No.  i. 


kK^  I J  "J^lp^ 


c\^ 


m 


rr 


r-  ^ 


^n'-i>ig  i 


7 


«=^ 


Fundamental  harmonies. 


^ 


i 


^ itJ^ 


^ 


^ 


3 


^ 


6 


rt- 


CHAPTER  XVIII. 
also  the  first  eight  measures  of  his  Sonata,  Op.  2,  No.  3. 
Allegro  con  brio 


221 


^     rviic^iu  cun  orio. , . 


^ 


-Q. 


r  g  -  ' 


Fundamental  harmonies. 


^s 


-^^ 


^ 


? 


E 


6        6 
5 


This  exercise  of  analysis  should  be  practised  in  the  case  of  sim- 
ilar passages,  which  the  teacher  can  select. 

The  most  important  positions  for  chords  to  occupy  are  the  open- 
ing and  closing  of  the  entire  composition,  and  of  its  sections  and 
periods,  also  the  accented  parts  of  the  measures. 

The  dominant  chord  follows  long  after  the  tonic  chord  in  impor- 
tance ;  and  the  subdominant  chord  is  much  less  important  than  the 
dominant.  While  these  three,  collectively,  have  a  pre-eminence  over 
all  the  other  chords  of  the  scale,  which  warrants  the  common  classi- 
fication into  Primary  and  Secondary,  it  will  be  found  that  the  main- 
tenance of  the  existing  scale  is  effected  almost  entirely  by  the  pre- 
eminence of  the  tonic  and  dominant,  and  chiefly  by  that  of  the  tonic. 

So  long  as  this  pre-eminence  is  maintained  the  mind  retains  the 
original  scale,  and  when  the  normal  relation  of  principal  and  sub- 
ordinate chords  is  altered,  the  mind,  sometimes  at  once,  oftener 
gradually,  renounces  the  old  scale  and  adopts  a  new  one.  This  sub- 
stitution of  a  new  scale  is  called  Modulation.  The  assertion  of  the 
scale  ordinarily  occurs  in  the  very  first  chord,  and  the  scale  being 
adopted,  no  change  occurs  until  it  is  felt  that  the  tonic  chord  of  that 
scale  is  not  receiving  its  due  emphasis,  and  the  mind  casts  about  to 


222 


PARKHURST  HARMONY, 


determine  in  what  scale  the  normal  relations  of  the  chords  will  be 
restored. 

It  should  be  remarked  at  this  point  that  the  only  possible  method 
of  explaining  Modulation  is  to  make  it  evident  to  the  student 
what  his  own  mental  processes  are  in  this  proceeding.  Modulation 
is  a  spontaneous  act  of  the  mind  in  each  individual  listener.  He 
cannot  be  compelled  by  another,  he  cannot  even  compel  himself  at 
any  given  point,  to  modulate.  It  must  be  a  spontaneous  operation 
.induced  by  his  musical  sense  of  the  harmonies  in  their  relations  to 
each  other.  And  any  one  fully  understands  modulation  just  as  soon 
as  he  clearly  sees  how  his  own  mind  acts  in  the  process.  For  this 
reason  it  is  imperative  that  every  statement  here  made  should  be  fully 
verified  by  the  student,  by  examining  himself  to  find  whether  he  act- 
ually does  what  is  here  asserted. 

The  following  passage  would  be  judged  by  the  eye  alone  to  be  in 
the  key  of  C,  as  there  is  no  signature ; 


but  judged  by  the  ear,  which  knows  no  signature,  the  first  chord 
,  suggests  the  G-scale,  and  the  whole  passage  lies  consistently  in  that 
scale,  because  of  the  prevalence  of  the  primary  chords  of  the  scale, 
and  especially  because  of  the  emphasis  and  frequency  of  the  G-chord. 
And  yet  every  chord  of  it  belongs  equally  to  the  C-scale. 
If  a  piece  opens  as  follows: 


Allegro 


the  first  scale  suggested  is  the  G- Scale,  but  if  played  allegro,  this 
first  thought  is  dissipated  by  the  emphasis  that  falls  upon  the  C-chord 
in  the  second  and  third  measures,  which  would  be  an  unusual  chord 
to  emphasize  as  the  subdominant  of  G.  Yet  in  this  example  every 
chord  belongs  equally  to  the  G-scale.    The  foregoing  shows  that  any 


CHAPTER  XVIIL 


223 


passage  of  music  is  in  reality  in  that  scale  in  which  the  ear  interprets 
it  to  be,  independent  of  any  and  all  signatures. 

Suppose  a  principal  section  of  a  composition  in  the  key  of  C 
ends  with  a  complete  cadence  thus, 


¥  r  fH 


5Z: 


3X 


« 


/Cs 


^m 


thereupon  follows 


trrHtrfnTf^ 


m. 


J 


rifr.fff 


¥ 


^ 


The  musical  nonsense  of  beginning  a  new  division  of  the  piece 
with  a  chord  so  subordinate  as  that  of  the  subdominant,  induces 
the  mind  instantly  to  adopt  the  new  scale  of  F,  and  to  read  the  pas- 
j^ge  in  that  scale,  although  it  contains  not  a  single  chord  foreign  to 
the  old  C-scale.  F  now  takes  the  coloring  of  the  tonic,  and  C  that  of 
the  dominant. 

;.•  Thus  far  we  have  said  nothing  of  accidentals  as  a  means  of  mod- 
ulation, for  WQ  have  used  none.  The  common  fallacy  of  supposing 
that  modulation  hinges  upon  the  use  of  tones  foreign  to  the  scale  is 
sufficiently  exposed  in  the  foregoing.  The  absence  of  accidentals 
cannot  prevent  a  modulation,  nor  their  presence  cause  one.  Modula- 
tion can  be  effected  instantly  and  easily  without  them,  and  on  the 
other  hand  they  can  be  introduced  numerously  without  our  feeling 
any  inclination  to  change  the  scale,  thus: 


ti^^'hi  'i'^^ 


ifc=# 


^ 


5 


t 


^'^S^lF^ 


•  This  is  not  saying  that  accidentals  are  not  frequently  of  very 
great  assistance  in  effecting  a  modulation,  nor  that  the  chords  in  the 
above  example  that  contain  them  do  not  offer  especially  favorable 
points  at  which  the  mind  cottld  be  diverged  into  a  new  scale.     But 


224 


PARKHURST  HARMONY, 


they  are  futile  in  themselves  to  accomplish  the  work.  The  musical 
sense  must  first  require  a  new  key  note  for  the  re-establishment  of 
the  normal  relations  of  principal  and  subordinate  tones  and  chords, 
before  a  modulation  can  take  place. 

Suppose  we  have  the  following  progressions, 
1. 


^m 


f 


? 


r 


m 


i 


f 


1=^ 


have  we  modulated  into  the  key  of  G?  Each  one  must  study  his 
own  feelings  to  determine.  If  one  person  says  he  has  utterly  given 
up  the  C-scale,  and  adopted  the  G-Scale,  then  for  him  it  is  a  complete 
modulation.  If  another  says  he  looks  upon  the  F#  as  a  substitute 
for  F  (producing  the  more  agreeable  major  chord  of  D)  and  that  he 
regards  G  as  still  the  dominant,  then  for  him  it  is  no  modulation.  If 
followed  immediately  by  this  phrase, 


^4-iJJj4^ 


i 


r^ 


^^^ 


i 


^ 


which  plainly  lies  in  the  C-scale,  and  the  two  passages  are  per- 
formed continuously,  doubtless  almost  every  one  will  read  the  first 
•as  lying  in  the  C-scale,  with  the  simple  substitution  of  F#  for  F. 
But  if  the  first  phrase  be  continued  thus, 


m 


I 


u 


* 


XlL 


P^ 


r     f    rr 


-O- 


TT 


XE 


«^ 


W 


^ 


the  above,  being  read  more  easily  in  G,  will  react  upon  the  closing 
part  of  the  first  phrase,  and  influence  one  to  the  adoption  of  the  G- 
scale.  That  is  to  say,  the  closing  part  of  the  first  phrase  is  ambigu- 
ous, and  ambiguous  phrases  arc  usually  interpreted  in  the  light  of 
what  follows.  This  ambiguity  of  a  phrase  (as  regards  its  key)  is 
one  reason  why  the  first  hearing  of  a  composition  is  more  difficult 


CHAPTER  XVllL  21^ 

than  the  second.  When  once  famiUar  with  the  piece,  the  mind  knows 
where  to  fix  its  modulations. 

It  is  easier  to  modulate  into  the  subdominant  than  into  the 
dominant,  (for  example  from  C  into  F,  than  from  C  into  G).  For 
if  the  G-chord  is  emphasized,  it  may  still  be  the  emphasis  natural  to 
the  dominant,  but  the  emphasis  of  the  F-chord  (a  comparatively 
subordinate  chord  in  the  C-scale)  so  disarranges  the  normal  relations 
in  the  C-scale  that  F  is  very  readily  accepted  as  a  new  tonic. 

Comparatively  speaking,  all  such  suspense  of  the  mind  is  of  in- 
frequent occurrence,  and  of  short  duration,  and  familiarity  with  the 
composition  results  in  assigning  definitely  to  one  scale  or  another 
many  of  those  passages  which  at  first  hearing  were  ambiguous. 
Still,  there  is  an  exhilaration  in  such  suspense  when  the  mind  is  not 
thereby  overtaxed,  whicli  is  one  of  the  many  devices  in  the  compos- 
er's art    for  preventing  monotony. 

Tlie  readiness  or  aversion  of  the  mind  to  interpret  an  ambiguous 
passage  in  a  new  scale  depends  greatly  upon  a  circumstance  which 
must  be  spoken  of.  At  the  beginning  of  a  piece  one  expects  a  clear 
announcement  and  somewhat  prolonged  maintenance  of  the  scale, 
and  very  early  in  the  composition  any  modulation  is  distasteful,  as  it 
evidently  mars  the  unity  of  it ;  but  after  a  time  the  original  scale  be- 
comes monotonous,  and  then  a  new  one  is  as  refreshing  as  before  it 
was  repellant.  The  mind  also  becomes  quickened  in  its  action,  as  the 
piece  continues,  just  as  it  does  under  any  sort  of  exertion  of  its 
powers ;  and  in  this  condition  modulations  can  be  effected  with  ease 
and  delight,  which  otherwise  would  be  laborious  and  painful.  And  in 
the  climax  of  vigorous  activity  the  mind  can  flit  from  scale  to  scale 
with  most  extraordinary  facility. 

We  now  proceed  to  speak  of  the  different  sorts  of  modulation, 
as  a  preparation  for  the  pupil's  own  practice  of  the  art. 

Scales  may  be  classified,  as  regards  their  relation  to  each  other, 
into  allied  and  foreign  scales.  This  is  for  convenience,  and  not 
strictly  accurate,  as  it.  suggests  a  radical  distinction  that  does  not 
exist,  for  nearly  all  the  scales  commonly  spoken  of  as  foreign  to  each 
other  really  possess  various  degrees  of  alliance.  The  alliance  of 
scales  consists  in  their  having  tones  in  common,  and  to  a  degree  the 
greater  the  number  of  tones  in  common,  the  closer  the  alliance.  Thus 
the  scales  of  G  major  and  F  major  are  the  most  closely  allied  to  C 
major,  as  the  tones  of  each  of  them  are  the  same  as  those  of  C,  with 
one  exception.  The  scale  of  D  has  two  tones  different  from  that  of 
C.  A  has  three  tones,  etc.,  until  finally  the  scales  of  C  and  CS  have 
not  a  single  tone  in  common.    Also  those  scales  that  have  the  most 


226 


PARKHURST  HARMONY. 


tones  in  common  have  several  fundamental  harmonies  in  common 
(compare  those  of  C  and  G),  while  the  less  closely  allied  scales  have 
only  single  tones  in  common. 

As  regards  modulation  into  ''foreign"  scales,  the  different  de- 
grees of  alliance  counts  for  little  or  nothing,  it  being  as  easy  to  pass 
from  the  key  of  C  to  that  of  Db  (these  two  scales  having  only  two 
tones  in  common)  as  from  C  to  D,  which  have  five  tones  in  common. 

The  scales  of  the  dominant  and  subdominant  of  any  key,  to- 
gether with  the  relative  major  or  minor  (as  the  case  may  be)  of  that 
key,  are  commonly  known  as  "the  related  scales"  of  that  key.  Thus 
the  "related  scales"  of  C  major  are,  A  minor,  G  major  and  F  major. 
The  related  scales  of  C  minor  are  Eb  major,  G  minor  and  F  minor. 
(Let  the  pupil  name  the  "related  scales"  of  several  different  keys, 
major  and  minor). 

1st.  Modulation  into  the  relative  major  or  minor  (as  from  C 
major  to  A  minor,  or  vice  versa). 

These  two  scales  are  so  nearly  allied  that  without  effort  one  i> 
able  to  hold  both  in  the  mind  simultaneously.  Their  relation  is  much 
closer  than  exists  in  the  case  of  any  other  scales.  This  closeness  of 
relation  is  well  illustrated  by  the  fact  that  the  syllables  of  the  major 
scale  (Do,  Re,  Mi,  etc.)  are  retained  for  the  same  tones  of  the  rela- 
tive minor,  so  that  the  key  note  and  the  dominant  of  A  minor  are 
called  "La"  and  "Mi",  instead  of  Do  and  Sol.  This  is  the  case  in 
the  so-called  "moveable-Do-system," — the  only  sensible  system,  by 
the  way — wherein  the  key  note  of  every  major  scale  is  called  "Do," 
and  the  fifth  of  the  scale  "Sol,"  etc.  Of  course,  in  the  "immovable- 
Do-system,"  (in  which  C  is  always  called  "Do,"  D  "Re,"  E 
"Mi"  and  so  on,  whatever  the  scale  may  be),  the  retention 
of  the  same  syllables  in  the  minor  scale  that  are  applied  to 
the  same  tones  of  the  relative  major  scale  does  not  so  signify  the 
close  relation  of  the  two  scales.  The  transition  from  a  major  to  its 
relative  minor,  or  vice  versa,  is  well  nigh  imperceptible.  Thus  G#, 
the  characteristic  tone  of  A  minor,  may  be  regarded  as  an  incidental 
substitute  for  G  in  the  scale  of  C,  and  the  following  chords, 


*  t. 


m 


^ 


m 


if  occurring  in  a  passage  evidently  in  A  minor,  would  be  regarded  as 
the  common  chords  on  the  4th,  5th  and  6th  of  that  scale;  but  if  the 


CHAPTER  XVlll.  227 

context  was  in  C  major,  they  would  be  thought  to  He  on  the 
2d,  3rd  and  4th  of  that  scale,  with  the  use  of  G#  to  produce  the 
stronger  major  chord  of  E.  As  a  matter  of  fact,  the  relative  major 
and  minor  scales  so  melt  into  each  other  that  it  is  impossible  to  use 
the  term  Modulation  in  respect  of  these  scales,  as  signifying  as 
much  as  where  there  is  a  more  radical  and  unequivocal  reconstruc- 
tion of  the  scale.  The  close  alliance  of  these  scales  makes  it  possible 
for  the  major  and  minor  complexion  in  faint  degree  to  sweep  in 
rapid  alternation  over  the  harmonies,  like  lights  and  shadows  over  a 
landscape,  and  the  mind  is  not  confused  by  the  labor  of  a  new  scale- 
construction.  Where  one  rhythmical  division  of  a  composition  ends 
plainly  in  major  or  minor,  and  the  next  begins  with  the  relative 
minor  or  major,  there  is  a  definiteness  in  the  assertion  of  the  new 
"mode"  or  quality  that  would  be  characterized  as  a  genuine  modu- 
lation. The  full  adjustment  of  the  matter  must  be  found  by  each 
student  through  the  examination  of  his  own  feelings,  as  he  listens 
to  the  alternation  of  these  scales.  The  interplay  of  major  and  minor 
is  perhaps  most  frequently  illustrated  in  chorals,  which  it  is  advis- 
able for  the  student  carefully  to  study,  and  then  compose  simple 
modulations  of  the  same  sort. 

26..     Modulation  into  the  other  "related''   {dominant  and  sub- 
dominant)  scales. 

A  great  many  of  the  so-called  modulations  into  the  dominant  and 
sub-dominant  keys  are  in  reality  not  so.  A  modulation  is  completely 
wrought  in  the  mind  only  when  a  new  tonic  is  indisputably  necessary 
for  understanding  the  harmonies.  But  the  harmonies  of  the  domin- 
ant and  sub-dominant,  and  especially  the  former,  having  already  fre- 
quent occurrence  in  the  old  scale,  and  thus  capable  of  ambiguity, 
longer  time  is  often  necessary  to  give  that  unequivocal  pre-eminence 
to  either  of  these  chords  that  shall  lead  the  mind  to  a  full  modulation. 
Accordingly  the  precise  point  of  modulation  into  these  scales  is  very 
often  indeterminate,  and  different  minds  will  modulate  at  different 
points.  The  difference  must  be  recognized  between  the  mere  sug- 
gestion of  a  new  scale  and  its  full  acceptance,  and  there  can  be  all 
degrees  of  emphasis  in  the  suggestion,  prior  to  its  acceptance.  A 
tonic-chord  is  emphasized  not  only  by  its  own  use,  but  by  the  use  of 
its  dominant-seventh  chord,  whose  resolution  is  so  naturally  into 
the  tonic-chord  that  one  seems  to  hear  the  latter  by  anticipation, 
— a  prophecy  of  the  tonic  in  the  dominant-seventh. 
Thus 


228 


PARKHURST  HARMONY. 


^^ 


30L 


the  first  chord,  on  D,  suggests  the  following  G-chord,  and  so  empha- 
sizes it,  and  similarly  the  C-chord  gives  emphasis  to  the  chord  on  F, 
by  its  almost  inevitable  resolution  into  that  chord.  Advantage  is 
taken  of  this  fact  to  emphasize  the  chord  which  it  is  desired  shall 
be  taken  as  the  new  tonic-chord,  by  having  that  chord  precede  which 
shall  find  its  most  natural  resolution  in  the  new  tonic-chord ;  that  is, 
the  dominant-seventh  chord  of  the  new  scale.  Thus  we  see  how  the 
accidental  (F#  in  the  first  case,  B^  in  the  second)  helps  to  the 
emphasis  of  the  following  chord,  and  thus  assists  the  modulation, 
while  powerless  of  itself  to  cause  it.  The  modulation  at  this  point 
is  as  yet  only  suggested,  even  if  the  harmonies  move  slowly,  and  the 
emphasis  of  the  new  tonic-chord  must  be  followed  up,  to  eflfect  a 
complete  change  of  scale ;  and  at  what  point  the  ambiguity  ceases, 
it  may  be  very  difficult,  and  perhaps  impossible  to  tell ,  thus : 

to  be  played  slowly. 


i 


*v 


m 


XE 


-ey- 


XE 


33: 


^ 


JOE 


« 


m 


-^^ 


^ 


-o^ 


33r 


XT 


^T" 


m 


^^,0  A^ 


XX. 


-t^ 


XE 


-O- 


<">- 


XE 


~r¥~ 


-€V 


ft=^ 

Aft 

tft 

A> 

0 

fS=q 

15- 
<> 

fS=i 

—^ 

4> 

<*■ 

ii 

— J 

*^ 1 

^            ** 

t> 

4T 

L-o 

4> 

^—4 

Where  similar  harmonies  follow  each  other  rapidly  there  may 
be  scarcely  the  suggestion  of  modulation,  and  if  the  sequel  is 
continued  in  the  old  key,  the  mind,  when  it  has  become  familiar  with 
the  music,  will  maintain  the  original  scale,  amid  all  the  accidentals 
which,  under  other  circumstances,  would  help  to  suggest  a  new  scale. 
This  IS  one  of  the  ways  in  which  a  person  understands  a  composition 
better  on  second  hearing — he  has  learned  how  to  interpret  some  pas- 
sages which,  as  regards  the  scale,  are  ambiguous,  and  is  helped  in 
reading  them  by  a  knowledge  of  the  sequel.    If,  as  sometimes  hap- 


CHAPTER  XVllI. 


219 


pens,  a  passage  will  give  equal  sense  in  the  original  and  in  the 
new  scale,  one  person  may  read  it  in  the  new,  another  in  tlie 
old ;  that  is,  one  modulates,  the  other  does  not.  Sometimes  by  a 
slight  alteration,  a  passage  that  belonged  plainly  to  the  original 
scale  can  be  read  in  the  new  scale,  when  that  scale  has  become  estab- 
lished in  the  mind,  and  a  peculiar  effect  of  identity  and  difference 
is  produced  ,  thus : 

irt  C.  -     -  .t   inG. 


^^^^^^g 


* 


i 


^^■Mt-±  -t 


ht^^ 


^^fS^Jl^ 


i 


;i 


^ffl 


Let  the  pupil  at  this  point  continue  his  study  of  modulation  in 
simple  vocal  and  instrumental  compositions,  with  special  reference 
to  the  modulations  into  the  dominant  and  sub-dominant  of  the 
original  key,  observing  how  they  are  sometimes  instantaneous,  some- 
times gradual :  and  then  let  him  connect  simple  chords  in  such  man 
ner  as  to  bring  him  from  his  original  scale  into  its  dominant  or 
sub-dominant.  His  first  eft'orts  may  be  crude,  but  with  continued 
practice  he  will  rapidly  acquire  the  technique  of  the  art. 

3rd.     Modulation  into  the  more  remote  scales. 

Modulation  into  the  "remote"  scales  is  much  less  frequent,  but 
far  more  striking  and  beautiful,  when  properly  introduced.  As  in 
such  modulation  there  will  be  none  of  that  ambiguity  such  as  we 
find  in  going  from  tonic  to  dominant,  there  will  be  little  or  no  diffi- 
culty in  obliterating  the  old  scale  and  establishing  the  new  one,  and 
in  this  respect  this  class  of  modulations  is  the  easiest.  On  the  other 
hand  it  is  at  the  same  time  difficult  to  make  a  satisfactory  modulation 
of  this  sort,  for  the  reason  that,  the  old  scale  being  obliterated  be- 
fore the  new  one  is  established,  the  harmonies  during  the  suspense 
must  with  special  consistency  and  musical  effect  cling  to  each  other, 
and  so  like  a  bridge  bear  the  hearer  over  to  the  firm  ground  of  a 
newly  established  scale.  Such  a  modulation  may  be  attained  more 
or  less  quickly,  according  to  the  wish  of  the  composer  and  the  re- 
quirements of  the  situation  ;  either 

1st,  Instantaneously, 


I  ^  jj !«  ii^'-'-i 


i 


^ 


s 


s 

-€»- 


230 


PARKHURST  HARMONY. 


which  is  technically  called  a  "transition,"  and  occurs  most  frequent- 
ly in  passing  from  any  major  scale  to  that  which  lies  a  major  third 
belozv  (as  in  the  example),  and  is  most  conclusive  when  the  "transi- 
tion" occurs  at  the  beginning  of  a  new  rhythmical  division  of  the 
composition ;  or, 

2d,  by  means  of  one  intermediate  chord   (often  the  dominant- 
seventh  chord  of  the  new  scale). 


^^ 


^ 


Db 


Dt 


^ 


m 


m 


tiF 


acy— Jz 


m 


'>' .]  rf\T 


* 


i 


3X 


o- 


As  a  most  serviceable  intermediate  chord  we  can  avail  ourselves 
of  either  of  the  chords  containing  an  augmented  sixth  (the  aug- 
mented sixths  the  augmented  sixth-and-fifth,  and  the  augmented 
sixth-fourth-and-third),  as  the  resolution  of  these  chords  brings  us 
to  a  harmony  which  can  readily  be  interpreted  as  the  tonic  harmony 
(often  in  the  second  inversion,  as  a  J  chord)  of  a  new  scale.  The 
pupil  is  advised  to  make  a  careful  review  of  the  chords  con- 
taining the  augmented  sixth,  and  he  will  find  that  those  founded 
on  the  third  and  on  the  sixth  of  the  scale,  which  are  unser- 
viceable when  the  composition  is  to  remain  in  the  old  scale,  are  very 
valuable  as  a  means  of  modulating  into  foreign  scales.  But  it 
is  to  be  observed  .that  when  we  modulate  (as  said  above)  by  means 
of  on£  chord,  although  the  harmony  following  that  chord  is  very 
naturally  accepted  as  the  tonic  or  dominant  harmony  of  the  new 
scale,  yet  the  new  scale  is  not  so  absolutely  unequivocal,  that  violence 
is  done  to  the  feelings  if  the  following  harmonies  bring  us  out  into 
still  another  scale. 

The  use  of  the  several  chords  containing  an  augmented  sixth  m 
effecting  modulation  is  illustrated  in  the  following: 

from  C  major  to  A  minor.        C  major  to  B  minor. 


--^*3 — 'HH— 

;iz^:z:#==fe=i%| 

4 ^^-^4f ^ 

^ — ' — 1 — 1 — 

■     1    1 

p h«4 

CHAPTER  XVllL 


231 


C  major  to  E  minor. 


C  major  to  B  major 


^ 


i 


<^ 


f-fp 


f 


zt 


^ 


H 


PB= 


^ 


XE 


XH 


-O- 


5 


The  modulation  is  effected  at  the  ^  chord  into  which  the  aug-- 
niented  chord  resolves.  If  the  pupil  plays  the  examples  slozvly  and 
attentively,  he  will  feel  the  root  of  the  chord  to  be  the  tonic,  and 
the  hass  to  be  the  dominant,  of  the  new  scale.  By  giving  to  this 
resolving  J  chord  a  major  third  (instead  of  a  minor  as  above),  we 
modulate  instantly  into  the  major  scales  founded  upon  the  same 
letters ,  thus : 


into  A  major. 


i  \i  h 


XE 


XE 


W 


XE 


-^ 


^ 


i 


m 


^ 


XE 


into  B  major. 


m 


^ 


^m 


i    i  jA  j}i   j^ 


')   "      1^ 


There  are  still  other  modulations  through  the  intervention  of  a 
single  chord : 

to  F  minor. 


I 


#; 


re 


1 


^p^ 


232 


PARKHURST  HARMONY. 


toE 


minor. 


F^f«; 


P 


X 


» 


xs: 


i 


to  Et  major. 


to  E    major. 


i 


xc 


lg 


#^ 


^rrs^    ^ 


XT 


m: 


m 


r  if  r 


3X 


The  above  modulations  are  not  all  equally  successful  in  fully  es- 
tablishing the  new  scale.  A  modulation  that  is  attempted  with  the 
intervention  of  only  one  chord  is  always  more  successful  with  a 
slo7v  movement  of  the  chords,  as  the  mind  thus  has  time  to  prepare 
for  the  change  of  scale.  The  reiteration  of  the  intermediate  chord, 
either  identically  the  same,  or  with  more  or  less  change  in  the  posi- 
tion of  the  voices,  will  usually  make  the  modulation  perfect;  thus, 
the  last  of  the  above  examples  can  be  in  this  manner  prolonged,  yet 
without  using  any  essentially  new  harmonies,  and  the  modulation  in- 
to E  will  be  unequivocal ,  as  follows : 


^ 


xx. 


i 


i 


xr 


Any  modulation  which  would  appear  hasty  if  the  intermediate 
chord  were  at  once  followed  by  the  new  tonic  harmony,  can  be  made 
satisfactory  by  this  method  of  reiteration  and  delay,  and  the  pupil 
is  advised  to  practice  the  art  of  prolonging  the  modulating  chord, 
by  changing  the  position  of  the  several  voices,  with  special  attention 
to  the  melodic  character  of  the  soprano,  which  will  divert  attention 
from  the  sameness  of  the  harmony. 

3rd.     Modulation  by  means  of  more  than  one  chord. 

No  new  principle  is  herein  involved.  Instead  of  accepting  the 
next  chord  following  the  first  foreign  chord  as  the  tonic  or  dominant 
of  the  new  scale,  the  composer  does  not  settle  upon  that  key,  but  in- 
troduces one  or  more  chords  wliich  compel  the  hearer  to  gravitate 


CHAPTER  XVllL 


233 


into  a  different  scale  from  the  one  first  suggested.  Thus  there  may 
be  a  mere  glancing  at  different  scales,  fully  accepting  only  the  last 
one  into  which  the  foreign  chords  lead,  or  sometimes  there  may  be 
a  distinct  modulation  into  a  new  scale,  followed  immediately  by  a 
distinct  modulation  into  still  another.  Circumstances  must  deter- 
mine the  propriety  of  this  prolonged  suspense  and  special  effort 
of  the  mind.  What  would  prove  a  shock  to  the  feelings  near  the 
beginning  of  a  composition,  is  often  a  pleasurable  sensation  after- 
ward, to  relieve  the  monotony.  In  many  cases  it  will  remain  an  open 
question  whether  there  be  several  distinct  modulations,  or  whether 
a  number  of  new  scales  have  been  only  more  or  less  strongly  sug- 
gested. 

The  following  examples  will  suffice  to  illustrate  this  last  sort  of 
modulation. 


to  Fj^  nfiinor. 


I 


i 


U 


b. 


to  D  major. 


u 


^ 


^m 


XE 


^? 


^ 


a^i 


2SS 


w-1 


?^^ 


^   ^ 


m 


\?p  \)fj 


rf¥ 


V-W 


^>    l#p  \ 


to  C^  minor. 


i^ 


c. 


-o- 


XE 


i 


^ 


^ 


M 


W 


4^ 


^^ 


V=\ 


m 


y^ 


i 


^»\^ 


¥ 


f 


tec 


d. 


to  D  minor. 


to  E\>  minor. 


M 


fjfjf 


-^ 


s 


m 


:#^ 


o 

^ 


feM 


«■    -^  ^ 
^ 


tJ 


U 


g 


m 


-o- 


y-i;^>  feg 


*^*s^ 


p^ 


Izo: 


^^^r^ 


"jiz: 


xm 


^^p- 


WDE. 


234 


PARKHURST  HARMONY. 


Enharmonic  Change. 

In  the  second  measure  of  the  foregoing  ilkistrations  (a)  and 
(b),  the  tone  that  is  expressed  by  Ab  in  alto  is  continued  in  the  next 
measure,  but  thcie  expressed  by  G#.  This  is  for  the  sake  of  having 
the  notation  express  to  the  eye  the  proper  relation  of  the  tone  in 
the  chord  to  which  it  belongs;  The  harmony  of  the  third  measure 
is  a  common  chord  founded  upon  C#,  the  fifth  of  which  chord  is 
G#,  not  Ab.  Such  a  change  is  called  enharmonic  change,  and  may 
occur  in  several  voices  simultaneously,  thus; 


It  is  an  interesting  fact  that  even  after  a  new  scale  has  been  per- 
fectly established,  and  the  old  one  apparently  forgotten,  there  is 
still  a  lingering  memory  of  it  in  the  mind,  so  that  it  is  easier  to  re- 
assert the  old  scale  again  than  to  pass  into  any  other.  In  accord  with 
this  fact  is  the  requirement  that  in  general  a  composition  should  end 
in  the  same  scale  in  which  it  began,  to  maintain  the  proper  unity 
of  the  composition  ;  and  yet,  between  the  beginning  and  the  end,  the 
mind  may  have  perfectly  established  itself  in  a  dozen  different 
scales. 

Probably  the  simplest,  least  obtrusive,  and  most  successful 
method  of  passing  into  a  remote  scale  is  by  changing  the  third  in  the 
triad  from  major  to  minor,  or  from  minor  to  major,  in  a  succession 
of  slow  harmonies,  thus  : 


to  AV  major. 


to  G  minor. 


k>     rWi^i 


M 


-^  l^j.  i'-^  ^'^g  I'-n  lt.-§  l^'-L^  4-r^-^ 


^S 


ODE 


O     i    4»— i     i¥      I  \, 


km     II   *»      I    *M   «» 


iX 


to  D  minor. 


CHAPTER  XVIII. 


233 


I 


M 


^m 


IT-Tf C» 


ff 


W 


m 


XE 


xr 


By  progressing  slowly  the  mind  easily  adopts  the  new  scale,  but 
if  the  harmonies  follow  rapidly  the  modulation  is  too  abrupt.  This 
change  is  best  made  in  the  tonic-chord  of  the  first  scale,  but  it  can 
also  be  made  in  the  dominant  and  sub-dominant  chords.  If  the  pupil 
has  had  little  or  no  practice  in  modulating,  he  is  advised  to  find 
his  modulations  on  the  piano,  starting  with  the  key  of  C,  and  wan- 
dering off  into  other  scales  without  predetermination  as  to  the  scale 
into  which  he  will  come  out.  Having  found  a  good  modulation  from 
C  into  any  other  scale,  let  him  then  use  the  same  formula  in  modula- 
ting from  G  and  from  other  scales.  This  is  exceedingly  good  prac- 
tice, and  he  will  soon  modulate  as  readily  from  any  scale  as  from  C. 

In  connection  with  his  own  efforts  in  modulation,  the  pupil 
should  also  study  the  works  of  the  best  composers,  to  cultivate  his 
taste  for  the  finest  methods  of  introducing  new  scales. 


Summary. 

The  intelligibility  of  music  requires  what : — The  predominant 
tones  and  chords  of  a  scale: — The  most  important  positions  for 
chords  to  occupy : — How  a  scale  is  maintained : — Adoption  of  a  new 
scale  caused  by  what,  and  called  what : — Modulation  not  dependent 
upon  accidentals : — How  ambiguous  phrases  are  usually  interpreted : 
— Why  easier  to  modulate  into  sub-dominant  than  into  dominant : — 
In  what  parts  of  a  composition  one  has  aversion  and  inclination  for 
modulating: — Meaning  of  "allied"  and  ** foreign,"  as  applied  to 
scales : — Which  are  called  "allied"  or  "related" : — Close  relation  of 
major  and  its  relative  minor : — Why  the  precise  point  of  modulation 
into  the  dominant  or  sub-dominant  is  so  often  indeterminate: — A 
scale  can  be  suggested  without  being  adopted : — Why  it  is  both  easier 
and  more  difficult  to  modulate  into  the  "remote"  scales : — The  most 
frequent  case  of  "transition" : — W^hat  chords  especially  serviceable  in 
modulation  : — Enharmonic  change  : — The  old  scale  not  utterly  oblit- 
erated :— Modulation  by  changing  major  chord  to  minor,  or  viee 
versa. 


36 


PARKHURST  HARMONY. 


CHAPTER  XIX. 

Modulation  (concluded).     Chromatic  Chords. 

The  varieties  of  modulation  are  inexhaustible,  and  a  critical  taste 
will  reject  all  such  as  are  crude  and  mechanical.  The  finest  of  all 
cannot  be  realized  in  a  detached  passage  of  three  or  four  meas- 
ures. Their  appropriateness  is  recognized,  and  their  beauty  en- 
hanced, by  the  circumstances  under  which  they  occur.  The  art  of 
changing  the  scale  is  one  that  requires  long  and  patient  practice,  as 
it  admits  of  the  greatest  skill  and  delicacy.  Its  mastery  can  be 
anticipated  only  after  the  pupil  has  carried  his  studies  far  beyond  the 
province  of  Harmony.  The  difficulties  of  the  subject  must  be  an 
incentive,  not  a  discouragement,  to  the  cultivation  of  a  refined  taste 
for  this  most  subtle  fruit  of  the  composer's  skill. 

Formulae  of  modulation  are  of  little  worth;  at  best  they  only 
illustrate  the  method  and  principle,  and  help  the  student  to  acquire 
the  technique  and  spirit,  of  the  art.  The  following  illustrate  the 
method  of  passing  from  C  major  to  every  other  major  scale,  and 
from  A  minor  to  every  other  minor  scale. 

After  playing  them  attentively,  let  them  be  transposed,  by  be- 
ginning upon  other  major  and  minor  scales.  The  analysis  of  modu- 
lations in  standard  compositions  is  also  excellent  and  interesting 
discipline.  But  above  all  the  student  is  urged  to  develop  his  own 
power,  in  the  discovery  of  other  progressions  whereby  to  reach 
related  and  remote  scales. 


Six  diatonic  major  modulations  from  C  major. 

^^^  ^-J.i  1(11  C  toE. 

-<SL 


M^^Mt^ 


k^UfJ- 


o  118  " 


3X< 


^^t?sti^^Ep^ 


M  d4  4$^i 


i^-rrp  i^p  ni 


^iMA 


M 


-o- 


f 


JOE 


C  toF. 


Cto  G 


CtoA 


IP 


I 


2Z 


Tn 


Tjr 


o 


tfP  \ 


r 


CHAPTER  XIX. 
C  toB. 


237 


fw^f^ 


m 


n 


m 


tfn^ft-f^-  '^  i»'jiC 


XE 


o    "  SSt^- 


A 


J 


1^ 


A 


^ 


m 


«i? 


¥ 


3DC 


¥ 


f  «f  rf 


Five  chromatic  major  modulations  from  C  major. 

C  to  Dk  CtoEt. 


i 


zz 


m 


^ 


2cr 


Snr 


^ 


^ 


^ 


<^   I  11 


fe 


fe 


^  t>p  u  ..  .fd  .K-J 1,  J 


ffi 


H;    «* 


? 


^ 


f 


^y 


I 


CtoGUor  F^) 


M 


Cto  At, 


=^ 


xr 


<»        m 


«^ 


^ 


XE 


PR 


XH 


1^1^^  |bJHu  ,i,¥>ij^i'n  ||fY|¥'!r|-^ 


g 


C  to  Bb. 

A  ,!,„  iij  4^  ir"^  '^r^f  l^k  J 


rr^r  " 


g 


¥ 


br^       P 


Six  diatonic  minor  modulations  from  A  minol*. 


y "  ^.-  A  to  c. 

ft  J'liVii,.iiVii,.^^i#4 


^^ 


w 


^m 


* 


238 


PARKHURST  HARMONY. 

A  to  D: 


^ 


m 


iil^ 


XH 


f 


^ 


s 


4v   r-' 


i9- 


XE 


f^ 


22 


A  to  E: 


p  ^  P  i  If 


^ 


AtoF 


j  ^jTrl '  J I 


3a: 


f^ 


^ 


'iTfTir 


i 


i 


/?     P<? 


P         py 


XE 


^ 


Ato  G 


^ 


p3t^ 


fur '  Ff  t^fw 


3Cf: 


G a 


r  f^  |tf 


g 


^ 


-e>- 


XJ" 


Five  chromatic  minor  modulations  from  A  minor. 

AtoBK         .      I  AtoC#. 


m 


#R^ 


^^^fe  ni(tij#^ 


fe 


Jf::^=:S: 


n !» 


Bf2 « 


t>o     II I    *^r   I    $°  ijg 


C  to  El.. 


Mi^  I'xiwjh^N^^M^^ 


Ato  F^: 


«1F 


IX 


^ 


i 


331 


zt^ 


A  to  G;t 


V  Hf  ll-l  I  J »')  j 


ig —  r-^    (^ 


1^ 


;o- 


CHAPTER  XIX. 


239 


^A  very  peculiar  chromatic  series  of  chords,  favorable  for  modu- 
lation, is  that  in  which  the  bass  is  a  continuous  downward  chromatic 
scale,  while  the  three  upper  parts  alternately  move  in  an  ascending 
chromatic  scale,  the  entire  series  consisting  of  the  three  chords, 
J,  2,  7,  repeated  over  and  over.  Each  chord  can  be  the  initial  one 
for  a  modulation.  Let  the  pupil  determine  into  what  scales  he  can 
pass  from  the  several  chords. 


U)    (2)  (3)     (4)     (5)     (6)      (7)    (8)    (9) 


^^^f^rWW 


etc. 


.v"j  r'r  fitf^jiiJ  >%ii,.)^jyj  ji^ 


A  quick  transition  from  scale  to  scale  is  sometimes  desirable,  as 
in  a  sprightly  movement  like  the  following: 


in  F  major 


in  F  minor. 


in  A\>  major 


in  A\>  minor. 


^w 


A  slow  harmonic  movement,  more  or  less  elaborated,  pro- 
longs the  passage  into  the  new  scale  in  a  very  effective  manner,  as  in 
the  following,  where  we  pass  from  the  key  of  C  to  that  of  Ab,  the 
modulation  being  complete,  although  we  have  only  reached  the 
dominant  seventh  of  the  new  scale.  Indeed,  the  tonic  chord  of  the 
new  scale  must,  as  a  rule,  be  avoided  until  the  scale  is  fully  estab- 
lished. 


I 


Allegro 


?=^ 


-^ 


spg^ 


^ 


7 


? 


F 


f 


240 


PARKHURST  HARMONY. 


In  the  following,  modulation  is  instantly  induced  by  the  fact  that 
the  mind  regards  the  first  chord  of  the  second  and  of  the  third 
phrase  as  standing  in  the  same  scale-relation  as  the  first  chord  of 
the  first  phrase.  Hence  Ab  minor  and  E  minor  are  at  once  regarded 
as  keynotes  of  new  scales. 


By  successive  modulations  into  the  dominant,  one  can  pass 
through  the  entire  circle  of  scales,  coming  back  to  the  original  key. 
As  examples  of  this  sort  of  exercise  see  Beethoven's  "Two  Pre- 
ludes," Op.  39.    The  first  part  of  No.  2  is  as  follows : — 


^^g 


^ 

F 


l^fl^f 


n 


f 


j^,j|j-_j> 

m 


r<--T 


m 


i 


m 


^ 


CHAPTER  XIX, 


241 


^ 


uAimi 


^ 


^f 


PTtf 


s 


^ 


m 


k 


g 


*^:g   I* 


I 


? 


^ 


P 


ud 


^^ 


^ 


fp^ 


'y-h^y^ 


u 


^^ 


e 


^ 


5 


^ 


^^W 


^^ 


jtAJJ*^ 


a 


^ 


ip^- 


^¥^ 


etc. 


tt 


^ 


^ 


^ 


s 


Such  a  form  of  composition  cannot  be  a  great  work  of  art,  but 
it  is  a  profitable  exercise  for  the  student. 

In  some  chromatic  progressions  one  may  lose,  for  a  time,  all 
idea  of  a  scale,  and  at  any  point  a  scale  may  be  established.  Such 
suspension  of  all  scale  relation,  however,  can  be  only  of  rare  occur- 
rence and  of  brief  duration. 


:.in7\\^,^m 


,i 


^^, 


P 


!^     f-ffl» 


242 


PARKHURST  HARMONY. 


Without  producing  a  modulation,  it  is  possible  to  use  all  varieties 
of  chromatically  altered  chords,  as  follows: — 


^ 


^^  -J  J  w^-^H^ 


t\>f\h  fpf  I'lf  r 't  fflr 


? 


Let  the  pupil  acquire  all  the  skill  possible  in  forming  elaborately 
chromatic  chords.  Improvisation  will  lead  to  the  discovery  of  many 
beautiful  and  striking  effects.  But  it  is  an  embellishment  that  is  to 
be  used  with  great  discretion.  Excess  makes  a  composition  florid,! 
[but  weak  and  diffuse.  Strength  of  musical  thought,  as  of  all  other 
thought,  has  simplicity  as  a  main  clement,  and  the  enduring 
music  of  the  world  shows  a  masterly  preponderance  of  the  simplest 
harmonies.     Learn  to  use  chromatics — then  learn  to  avoid  them!    yC 

CHAPTER  XX. 
Cadences. 
A  "cadence"  is  a  point  of  rest.  The  word  means,  Hterally,  a 
"falling,"  and  in  its  technical  use  involves  the  idea  of  the  "gravita- 
tion of  chords"  to  that  one  in  the  scale  upon  which  the  mind  can 
completely  rest,  i.  e.,  the  tonic  chord.  The  most  complete  cadence 
therefore  consists  of  the  tonic  chord,  emphasized  by  being  preceded 
by.  that  chord  which  leads  most  naturally  into  the  tonic,  and  thus  as 
it  were  expresses  it  by  anticipation  ;  i.  e.,  the  dominant  chord.  With 
the  seventh  added  (forming  the  dominant-seventh  chord)  the 
resolution  into  the  tonic  is  more  emphatic,  and  the  formula  for  the 
most  perfect  cadence  possible  is  as  follows: 

a; 


Complete  cadence, 


i 


3 


XH 


-cv 


m 


3nE 


Not  a  cadence, 


^0 


CHAPTER  XX. 


243 


The  essentials  for  the  completeness  of  this  cadence  are  that  the 
tonic  chord  shall  occur  in  the  accented  part  of  the  measure  (com- 
pare the  above  (a)  and  (b)),  that  each  chord  shall  be  in  its  funda- 
mental position,  and  that  the  tonic  chord  shall  have  the  tonic  in  the 
soprano. 

The  Authentic  Cadence. 

Any  dominant  or  dominant-seventh  chord  (unaccented),  fol- 
lowed by  the  accented  tonic  chord,  constitute?  what  is  called  the 
"authentic  cadence/'  This  is  in  several  varieties .  thus : 


i 


5 


XE 


3DE 


S 


-O- 


complete         incomplete,    incomplete.         inc. 


■^►- 


mc. 


XE 


XE 


C. 


H 


3a: 


^ 


23 


-€>- 


3? 


tt 


-O- 


^ 


XT 


inc. 


inc. 


TT 


inc, 


■ST 
inc, 


3lSL 


XE 


XE 


XE 


f 


6 


6 


That  is,  any  deviation  of  either  chord  from  the  formula  ex- 
pressed above  (viz.,  the  dominant  or  dominant-seventh  chord,  in 
fundamental  position,  followed  by  the  accented  tonic  chord  in  fun- 
damental position  with  the  tonic  in  soprano)  is  still  an  authentic 
cadence,  but  is  called  incomplete,  and  the  aforesaid  formula  is  called 
the  complete  authentic  cadence. 

The  above  will  suffice  for  the  general  classification  of  the  Au- 
thentic cadences ;  but  it  is  to  be  observed  that  the  more  we  depart 
from  the  formula  of  the  most  perfect  cadence,  the  less  of  a  feeling 
of  cadence  (i.  e.,  a  point  of  rest)  there  will  be.  Thus  there 
is  very  little  of  the  cadence-feeling-  when  the  tonic  chord  is 
expressed  in  its  first  inversion  (as  at  (a),,  (b)  and  (c)  above), 
and  such  a  use  of  the  chords  would  hardly  ever  occur,  where  the 
effect  of  a  cadence  is  required.  When  the  tonic  chord  is  expressed 
in  its  second  immersion  (as  at  (d)  and  (e)  ).  there  is  absolutely  no 
cadence  feeling,  as  the  J  chord  can  never  be  a  point  of  rest.  To 
be  serviceable  as  an  '"incomplete  cadence"  the  tonic  chord  is  almost 


Z44 


PARKHURST  HARMONY, 


invariably  in  its  fundamental  position.  The  desirability  of  having 
different  degrees  of  completeness  in  the  cadence-feeling  will  be  ex- 
plained later. 

The  Plagal  Cadence. 

The  unaccented  sub-dominant  chord,  followed  by  the  accented 
tonic  chord,  is  called  the  Plagal  cadence : 


I 


3x: 


ic 


^ 


^ 


^ 


■«»- 


ve 


^ 


1 


^ 


XH 


xr 


3nr 


(These  are  all  Plagal  cadences,  and  the  distinction  of  "complete" 
and  "incomplete"  is  not  so  important  as  in  the  authentic  cadences, 
but  both  chords  are  usually  in  fundamental  position.) 

This  cadence,  as  the  close  of  a  composition,  is  rarely  used  alone, 
but  is  generally  preceded  by  the  authentic  cadence ,  thus : 


^^ 


-r%- 


XE 


& 


anthentic 


xn 


plagal. 


XE 


XH 


XH 


— o — 

This  is  also  called  the  "Amen  cadence,"  as  it  is  the  one  commonly 
used  for  the  "Amen"  after  the  last  verse  of  Church  hymns. 

The  Half  Cadence. 

This  occurs  when  the  dominant,  instead  of  the  tonic  chord,  is 
placed  in  the  accented  part  of  the  measure,  and  is  preceded  either 
by  the  tonic  chord,  or  by  any  other  that  naturally  leads  into  the 
dominant,  thus: 


CHAPTER  XX. 


245 


We  can  rest  on  the  dominant  chord  longer  than  on  any  other, 
except  the  tonic ;  and  that  form  of  the  half  cadence  will  give  the 
strongest  feeling  of  cadence,  in  which  the  dominant  chord  is  pre- 
ceded by  such  a  chord  as  leads  most  evidently  into  the  dominant, 
that  is,  when  preceded  by  its  ozi'ji  dominant  or  dominant-seventh 
chord,  as  at  (a),  (b),  (c)  and  (d).  This  is  not  a  modulation,  as  has 
been  explained  in  the  preceding  chapter,  but  a  casual  use  of  the  ac- 
cidental, which  of  itself  cannot  produce  a  change  of  scale. 

The  Deceptive  Cadence. 

This  is  produced  when  the  unaccented  dominant  chord  is  fol- 
lowed by  any  other  than  the  tonic  chord ;  thus : 


f^  l»  U  l» 


^ 


f 


TJ  ZZ 


XE 


JOE 


r 


This  is  called  a  "deceptive"  cadence,  because  the  tonic  chord  is 
the  one  that  most  naturally  follows  the  dominant,  and  the  above 
progressions  are  somewhat  unexpected.  Yet  the  unexpected  is  not 
necessarily  the  unsatisfactory,  but  often,  on  that  very  account,  the 
more  pleasing. 

In  addition  to  all  the  foregoing  cadences,  a  certain  degree  of  the 
cadence-feeling  can  be  produced  by  the  use  of  any  common  chord 
in  the  scale,  when  preceded  by  a  chord  that  leads  strongly  into  it. 

b. 


-o- 


H 


H 


S 


« 


bad. 


good. 


bad 


good. 


^^ 


F^ 


-o- 


m 


c. 


d. 


e. 


XE 


351 


3x: 


m-. 


bad. 


good. 


^^ 


f 


good. 


good, 


-^ 


f 


XE 


^ 


XE 


In  (a)  and  (b)  the  final  chord  is  emphasized  in  being  preceded 
by  a  chord  that  almost  inevitably  leads  into  it,  and  thus  a  degree  of 


246 


PARKHURST  HARMONY. 


cadence-feeling  is  created.  A  major  scale  and  its  "relative  minor," 
and  vice  versa,  He  so  closely  together  in  the  mind,  that  the  passage 
from  one  to  the  other  involves  no  effort,  and  (c),  (d)  and>  (e)  may- 
be felt,  (c)  as  an  authentic,  (d)  a  half,  and  (e)  a  deceptive  cadence, 
in  A  minor. 

Below  are  presented  all  the  different  kinds  of  cadences. 


Cadences  in  C  Majok 
Dominant-Tonic  . 


H 


ffiB 


m 


3CE 


3X 


H 


^ 


^ 


o     g 


^ 


**  II  eP 


^ 


<^ 


complete. 


com 


plete. 


? 


Subdominant  -Tonic 


H 


acE 


XE 


^ 


5 


« 


^ 


% 


■9-  -*»- 


1!W=» 


§ 


3JE 


XE 


3Ci: 


^ 


Dominant 


S 


« 


« 


^^^ 


XT 


»'^   ^ 


"cy 


•o" 


^ 


XX 


XE 


Xfl 


§ 


4 
3 


f 


Dominant   — 


^   h">    11^ 


ffi 


> 


H 


XT 


-^^ 


^ 


3i: 


-o- 


-€V 


^ 


CHAPTER  XX. 


247 


i 


s 


«:  3 


?gff^^^ 


BF 


Jri"iir  r 


1    n^T 


i 


€> 


xs: 


.< 


ie:3 


6  7 


6    7 


The  last  three  may  he  regarded  as  respectively  authentic,  half,  and 
deceptive  cadences  in  the  scale  of  A  minor. 


Cadences  ik  A  Mikor. 

Dominant -Tonic. 


s 


m 


s 


n 


33 


XT 


XS 


<^ 


-*> 


dS' 


IE 


cojfiplete. 


*^ 


com 


m 


-e>- 


^ 


plete. 


XI 


n 


4 


1>     6 


i 


Subdomin  ant -Tonic. 


s 


XE 


3X 


g 


^ 


f 


f 


331 


xs: 


XE 


XE 


Dominant, 


i 


^Iro  Ihj  U^  II;: 


^ 


t«^i^g-4|« 


^      W^rr 


XT 


TT, 


^ 


33r=::^ 


^^ 


5    r  '  r 


Dominant -~ 


m 


XKE 


-€>■ 


XE 
XT 


M 


m 


s 


248 


PARKHURST  HARMONY, 


I 


i 


I? 


XE 


^ 


s= 


-cv 


jdc 


^^ 


iM 


^ 


o 


« 


^ 


4 


The  last  two  are  inconsistent  with  the  scale,  inasmuch  as  the  "lead- 
ing tone"  (G#)  is  sacrificed.  Nevertheless  they  can  be  used  in  a  composi- 
tion in  this  scale,  and  may  be  regarded  as,  respectively,  a  half,  and  an 
authentic  cadence  in  C  major. 


The  practical  use  of  cadences  will  be  best  understood  by  first 
understanding  that  a  musical  composition  is  not  a  constant  and  unin- 
terrupted succession  of  harmonies,  from  beginning  to  end,  like  the  in- 
cessant flow  of  a  stream.  A  musical  composition  is  an  orderly  suc- 
cession of  different  musical  ideas,  variously  related  to  each  other, 
conjoined,  and  yet  to  a  degree  disjoined.  It  is  analogous  to  a  liter- 
ary composition,  the  several  thoughts  of  which  are  also  variously 
related  to  each  other,  conjoined,  and  yet  to  a  degree  disjoined.  Thus 
the  literary  composition,  taken  first  in  its  entirety,  at  once  falls  into 
a  certain  number  of  chapters.  Each  chapter  has  its  subordinate 
divisions  in  the  form  of  sections,  or  paragraphs,  and  within  each 
paragraph  every  complete  idea  takes  the  form  of  a  sentence.  Last- 
ly each  sentence  is  usually  so  complex  as  to  contain  a  greater  or  less 
number  of  those  ultimate  organic  fragments  of  an  idea,  each  of 
which  is  called  a  phrase  or  clause. 

Thus  we  find  that  the  grand  idea,  expressed  by  the  entire  com- 
position, literary  or  musical,  is  minutely  subdivided ;  and  the  mind, 
in  the  conception  or  in  the  reading  of  the  work,  finds  a  point  of 
rest  in  the  progressive  development  of  the  idea,  wherever  it  finds  a 
distinct,  although  it  may  be  a  very  minute,  completion  of  that  idea, 
in  any  of  its  most  subordinate  details.  Thus  the  mind  is  frequently 
finding  the  cadence  throughout  the  entire  composition.  And  the 
cadences,  or  points  of  rest  successively  sought  and  gained,  are  al- 
ways commensurate,  in  their  duration  or  intensity,  with  the  relative 
importance  of  the  fragmentary  ideas  to  the  grand  idea.  The  marks 
©f  punctuation — the  period,  colon,  semicolon,  comma — in  a  measure 
express  to  the  eye  the  relative  duration  of  the  rest  or  cadence.  Ab- 
solute rest,  with  no  eflFo/t  of  the  mind  beyond,  can  come  only  with 
the  completion  of  the  work.  This  absolute  rest  is  found  only  in  the 
•'complete  authentic  cadence,"  the  ''full  period"  of  the  whole  idea. 


CHAPTER  XX.  249 

The  foregoing  cadences  are  very  unequal  in  the  degree  of  the 
cadence-feeling  excited  by  them,  and  are  thus  adequate  to  the  var- 
ious demands  for  cadence  in  the  development  of  the  musical  idea. 
It  is  not  to  be  supposed  that  the  various  chord-connections  in  the 
foregoing  list  of  cadences  always  produce  the  cadence  feeling.  Many 
of  them  are  used  frequently  without  any  sense  of  a  cadence.  The 
rhythmical  structure  of  the  composition  in  a  degree  creates  the  de- 
mand for  a  cadence  at  certain  points,  and  the  inherent  cadence  qual- 
ity of  certain  chord-progressions  thus  re-inforced  by  the  rhythmical 
demands  creates  the  sense  of  cadence  in  the  mind.  That  is  to  say,  the 
cadence-form  and  the  rhythmical  movement  are  conjointly  operative 
in  producing  the  sense  of  a  point  of  rest.  For  example,  the  domi- 
nant chord  occurring  in  the  beginning  of  a  measure,  and  preceded  by 
v^^hatsoever  chord,  cannot  invariably  create  the  cadence  feeling,  and 
yet  such  a  chord-progression  constitutes  the  ''half  cadence''  formula. 
But  if  the  rhythmical  structure  demands  a  cadence,  the  above  formula 
is  at  once  felt  to  be  a  point  of  rest.  The  rhythmical  movement  and 
the  cadence  formula  must  conspire  together.  And  the  less  of  the  in- 
herent cadence  quality  there  be  in  any  chord-progression,  the  more 
is  the  rhythm  determinative  of  the  sense  of  cadence  in  that 
progression.  The  mutual  interaction  of  the  rhythm  and  the  ca- 
dence formula  can  be  learned  only  by  practice.  But  the  foregoing 
table  of  cadence  formulae  should  be  carefully  studied,  as  only  in 
these  formulae  does  there  exist  any  of  the  inherent  cadence  quality. 
The  pupil  is  also  urged,  after  mastering  the  above  table,  to  study 
chorals,  which  more  clearly  illustrate  the  doctrine  of  cadence  than 
any  other  form  of  composition.  Each  line  of  a  choral  closes  with 
one  or  another  of  the  cadence  forms,  and  the  success  of  a  choral  de- 
pends in  no  small  degree  upon  their  judicious  alternation.  Other 
kinds  of  composition  can  also  be  studied  in  respect  of  the  use  of 
cadences,  but  this  presupposes  some  knowledge  of  the  art  of  con- 
structing a  composition,  which  is  learned  by  the  study  of  "musical 
form." 

As  the  concluding  exercise  of  this  chapter,  let  the  pupil  write 
examples  of  all  the  different  kinds  of  cadence  in  several  different 
keys,  major  and  minor. 

Summary. 

Meaning  of  cadence: — The  formula  of  the  most  complete  ca- 
dence:— Authentic  cadence,  complete  and  incomplete: — Plagal  ca- 
dence:— Its  use  with  authentic  cadence: — The  half  cadence: — The 
most  complete  half  cadence : — The  deceptive  cadence : — Why  so 
called : — Analogy  between  a  musical  and  a  literary  composition :— 


250  PARKHURST  HARMONY, 

Where  does  a  cadence  occur  in  both  forms  of  composition : — Intensity 
of  a  cadence  commensurate  with  what: — Cadence  feeUng  not  alv/ays 
produced  by  cadence  formula : — What  must  co-operate  with  the 
cadence  formula  to  produce  the  cadence  feehng: — The  use  of  ca- 
dence in  the  choral. 


In  conclusion,  a  few  words  as  to  the  treatment,  in  the  foregoing 
work,  of  the  voices  or  parts,  as  compared  with  their  treatment  in 
practical  compositions,  vocal  and  instrumental,  such  as  solos,  duets, 
trios,  choruses,  sonatas,  symphonies,  etc.  The  divergence  of  such 
works  from  the  form  of  all  exercises  in  this  book  is  so  great  as  to 
induce  the  feeling  in  many  minds  that  there  can  be  little  or  no 
relation  between  the  one  and  the  other,  and  the  undeniably  good  ef- 
fect resulting  from  the  violation  of  certain  rules  that  are  invariably 
insisted  upon  in  a  text-book  of  Harmony  (such  as  the  use  of  octave 
passages)  tends  to  weaken  one's  faith  in  the  validity  of  such  rules. 
The  confusion  all  arises  from  a  mistaken  idea  as  to  the  real  scope 
of  "Harmony,"  and  the  legitimate  application  of  its  rules.  The 
essentials  of  harmony  are  taught  therein,  but  not  the  numberless  de- 
tails of  effect  which  in  their  place  are  legitimate  and  necessary.  The 
foregoing  work  teaches  only  how  to  secure  the  fullest  harmonic  effect 
with  four  voices.  But  there  are  many  other  effects  highly  de- 
sirable in  music  beside  the  *' fullest  harmonic  effect  of  four 
voices."  The  prolonged  use  of  four  parts  in  this  manner  would 
soon  become  extremely  monotonous.  For  variety  of  effect  and 
relief  to  the  mind,  the  four  parts  must  sometimes  be  treated 
differently,  and  sometimes  a  less,  and  sometimes  a  greater  num- 
ber of  parts  must  be  used.  The  greatest  aggregate  of  musical 
effect  is  secured  by  proper  variety  and  alternation  of  means. 
So  that  there  is  an  important  place  for  unisons  and  octaves, 
for  solo,  duet,  and  trio,  for  full  chords  and  for  absolute  silence, 
as  well  as  for  the  "fullest  harmonic  effect  of  four  voices." 
The  acomplished  composer  must  be  familiar  with  every  device  that 
shall  enhance  the  effect  of  melody  and  harmony,  with  every  grouping 
of  the  tone-colors,  with  all  lights  and  shadows  that  shall  help  to 
realize  the  tone-picture.  In  view  of  such  a  goal,  the  work  accom- 
plished by  a  "text-book  of  Harmony"  seems  almost  insignificant.  In 
one  sense  it  is.  But  the  essential  principles  of  all  harmonic  combina- 
tion— the  most  important  thing  of  all — are  therein  learned,  and  the 
student  now  stands  one  step  beyond  the  threshold  of  the  art. 

Before  proceeding  to  the  next  department  of  theoretical  study — 
that  of  Counterpoint — it  is  in  most  cases  very  advisable  for  the 


CONCLUSION.  251 

student  to  make  a  thorough  review  of  the  entire  subject  of  Har- 
mony. By  so  doing,  he  will  be  amply  rewarded  in  the  more  complete 
understanding  of  all  the  fundamental  and  auxiliary  chords,  in  their 
construction  and  connection,  which  is  the  requisite  preparation  for 
success  in  musical  composition. 

In  making  a  review,  it  will  only  be  necessary  to  write  so  many  of 
the  exercises  in  each  section  as  will  give  proof  that  the  subject- 
matter  is  fully  mastered ;  and  it  will  be  much  more  profitable  to  use 
the  basses  as  exercises  in  **sight-reading,"  for  this  will  give  a  mas- 
tery of  the  chords  such  as  can  never  be  attained  by  merely  writing 
them.  In  the  review,  it  will  be  found  that  the  sense  of  the  chords  can 
be  imagined  much  more  easily  and  accurately  than  before;  and,  as  a 
final  word  of  counsel,  the  pupil  is  urged  to  cultivate  still  more  as- 
siduously this  power  of  knowing  the  effect  of  chords  without  playing 
them ;  for  without  it,  any  satisfactory  progress  beyond  the  province 
of  Harmony  is  impossible. 


25? 


PARKHURST  HARMONY, 


APPENDIX, 

The  discussion  of  questions  having  a  purely  theoretical  interest, 
and  without  any  practical  application,  in  the  study  of  Harmony,  does 
not  properly  belong  to  the  body  of  such  a  work  as  this,  and  has 
therefore  been  reserved  for  the  Appendix.  Other  questions,  of  un- 
doubted value  to  the  more  advanced  harmonist,  but  of  doubtful 
utility  to  the  beginner,  also  find  here  their  solution. 

(A) 
Full  List  of  Intervals. 


r  T^^ — I  1 

perfect,or  unison    tiut^ir.e nted       m  ajor 


Seconds.  * 

minor         augmented 


!<->. 


T3r 


^ 


Kf 


'  Thirds.  "  Fourths.  » 

major        minor        diminished  perfect    augmented  diminished 


tf"  \^^** 


* 


^ 


o- 


f 


XE 


i 


Fifths.  "  Sixths.  ^ 

perfect     augmented  diminished  major      minor      augmented 


S 


irrr 


jo: 


'  Sevenths.  '^  Octaves. 

major      minor      diminished  perfect   augmented    dittiinished 


XT 


aac 


[XE 


f 


$ 


Ninths.  ' 

major.  minor. 


Tenth. 


Eleventh. 
o — 


i 


Twelfth. 


Thirteenth.       Fo">-te«ith.       Fiftee^h. 


APPENDIX. 


23J»i 


Perfect  intervals. 
Prime. 

±                1 

Fourth. 

Fifth. 

Octave. 
^ i 

•!>                   Cl  Q 

4> 

o 

1 

Major  intervals. 

Second.  Third. 


Sixth. 


Seventh. 


Ninth. 


-€>- 


XE 


^^^ 

Minor  interv^als. 

Second.  Third. 


Sixth.         Seventh, 


Ninth. 


^ 


^ 


trrr 


Augmented  intervals. 
Prime.         Second. 


^ 


Fourth. 


Fifth. 


Sixth 


^ 


^ 


Diminished  intervals. 


I 


Third 


Fourth. 


Fifth. 


Seventh.        Octave 


^ 


€V 


* 


XH 


r^^ — ^ 


f 


For  all  simple  harmonic  purposes  the  intervals  of  a  ninth,  tenth, 
etc.,  are  the  same  as  a  second,  third,  etc.,  and  are  commonly  so 
named.  In  "Suspension"  the  ninth  is  distinguished  from  the  second, 
and  in  the  later  study  of  counterpoint,  the  tenth  and  twelfth  are 
sometimes  distinguished  from  the  third  and  fifth.  But  with  these 
slight  exceptions  all  intervals  are  reckoned  as  within  the  limits  of  an 
octave. 

(B) 

Reason  for  the  General  Use  of  Four-Part  Harmony. 

As  the  fundamental  combination  of  tones  in  Harmony  is  the 
"common  triad,"  it  might  be  supposed  that  our  elementary  chords 
would  be  "three-part  harmony."  This  is  not  the  case.  The  deter- 
mining factor  in  this  matter  is  the  consideration  that  such  a  number 
of  parts  will  inevitably  be  adopted  for  general  use  in  both  vocal  and 
instrumental  music  as  will  afford  the  most  satisfying  fulness  of 
harmony,  combined  with  the  requisite  simplicity  and  transpar- 
ency of  the  chords,  and  distinctness  of -the  individual  parts.  The 
aiumber   of  parts   in  the  chord   can   be  increased  indefinitely,  but 


?^4 


PARKHURST  HARMONY. 


beyond  a  certain  point  such  increase  tends  to  produce  fulsome 
harmonies,  and  a  sacrifice  of  simpHcity  and  distinctness.  A 
reduction,  beyond  a  certain  point,  in  the  number  of  parts,  on 
the  other  hand,  makes  the  harmonies  thin,  and  the  remaining 
parts  correspondingly  obstrusivc.  The  oppressive  richness  of 
full  chords  is  replaced  by  an  equally  oppressive  poverty  of 
scant  harmonies,  and  what  was  before  well-rounded,  through 
the  abundance  of  the  parts,  becomes  angular  through  their  scarcity. 

In  view  of  all  the  requirements,  the  most  satisfying  eflfects  are 
produced  by  four-toned  harmony.  This  is  not  to  the  exclusion  of 
five,  six,  seven,  and  eight-part  harmony,  on  the  one  side,  or  of 
three  and  two-part,  on  the  other  side,  but  in  the  nature  of  things 
four  is  the  normal  number.  Even  in  the  florid  harmonies  of  orches- 
tral music,  we  find  a  substratum  of  four  parts,  giving  the  basal 
chords  on  which  the  elaborate  superstructure  rests.  Our  vocal  music 
is  not  in  four  parts  because  we  have  soprano,  alto,  tenor  and  bass. 
On  the  contrary,  the  Creator  has  furnished  us  with  this  fourfold 
pitch  and  quality  of  the  human  voice  to  meet  the  harmonic  require- 
ments of  our  nature.  And  in  instrumental  music  the  acme  of  pure 
harmonic  enjoyment  is  found  in  the  "string  quartet." 


:  (C) 

Wherein  the  Distinctiveness  of  the  Parts  Consists. 

One  of  the  satisfying  elements  of  harmony  is  the  distinctive- 
ness of  the  several  parts.  This  distinctiveness  is  three- fold,  viz.,  dis- 
tinctiveness oi  pitch,  of  direction  of  movement,  and  of  rhythm. 

Suppose  the  bass  and  tenor  are  as  follows : 

oo 


£ 


XKE 


OO 


OO 


There  is  here  no  distinctiveness  at  all.  The  voices  are  in  unison. 
The  tone  is  stronger,  but  the  two  individualities  are  merged  into 
one.    But  in  the  following, 


P 


:«: 


Jt 


there  is  the  first  element  of  distinctiveness,  that  of  pitch,  but  their 
movement  and  rhythm  are  alike.    In  the  following, 


^ 

^ 


77    .^     ft 


APPENDIX. 


255 


the  two  voices  assert  their  individuahty  still  more  by  unlikeness  in 
their  direction  of  movement ;  and  in  the  following. 


we  find  the  three  elements  of  distinctiveness  combined,  viz.,  pitch, 
direction  of  movement,  and  rhythm.  Only  in  these  three  ways  can 
the  different  voices  or  parts  assert  their  individuality.*  In  the  exer- 
cises of  Harmony,  and  in  the  choral  style  of  composition,  the  individ- 
uality of  the  voices  is  almost  exclusively  confined  to  pitch  and  di- 
rection of  movement,  with  little  variety  of  rhythm.  The  highest 
voice  alone  is  treated  as  a  melody,  and  the  under  voices  have  little 
more  than  harmonic  significance.  The  fugue,  on  the  other  hand,  is 
the  highest  form  of  harmonic  writing,  because  each  voice  is  treated 
melodically,  and  in  addition  to  the  individuality  of  pitch  and  direc- 
tion of  movement,  is  also  as  rhythmically  distinct  as  possible. 

(D) 
The  Rel\son  for  the  Prohibitiox  of  Parallel  Perfect  Fifths. 

The  objectionableness  of  parallel  perfect  -fifths  is  evident,  but  har- 
monists have  ever  found  it  impossible  to  understand  and  state  clearly 
the  reason  for  the  objection.  The  following  statement  does  not 
pretend  to  be  original,  or  less  abstruse  than  previous  efforts  of  other 
writers. 

Every  chord  in  fundamental  position  has  its  boundary  line  or 
circle  expressed  by  its  root  and  fifth.  The  proper  connection  of 
chords  requires  a  sort  of  resolution  or  floi^'  of  one  chord  into  the 
next;  but  when  any  two  voices  express  the  fundamental  and  fifth 
in  two  successive  chords,  the  boundary  circle  of  each  chord  seems 
rigidly  maintained,  the  harmonies  are  in  contact,  but  they  do  not 
coalesce ,  thus : 


4    d{    I  [§ 


s 


^ 


«: 


S 


■a 


FO- 


i 


XE 


*This  is  presupposing-  the  same  quality  or  tone-color  in  the  parts  or  voices.  Variety  in  this 
respect  affords  another  valuable  element  of  distinctiveness,  to  be  sure,  but  we  are  here  con- 
cerned only  with  the  elements  involved  in  harmonic  structure. 


^56 


PARKHURST  HARMONY. 


In  seventh-chords,  the  occurrence  of  successive  perfect  -fifths  be- 
tween any  two  voices,  even  though  one  of  the  fifths  intervene  be- 
tween other  than  the  root  and  fifth  of  the  chord,  will  also  prevent 
the  coalescence  of  the  chords ,  thus : 


« 


pp 


In  the  diminished  fifth  there  is  not  the  same  effect  of  a  boundary 
circle,  and  it  can  be  made  to  follozv  a  perfect  fifth  (a)  ;  yet  the  eflPect 
is  not  good  if  it  precede  the  perfect  fifth  (b)  ;  still  the  progression 
from  diminished  to  perfect  fifth  is  by  some  good  writers  allowed 
.between  the  inner  parts  (c). 


I 


i 


b. 


^^ 


s 


-€>- 


^ 


goad, 


bad.  tolerab 


i 


PP 


ICE 


i 


6: 


tolerable. 


The  foregoing  statement  concerning  parallel  fifths  is  far  from 
conclusive.    This  is  frankly  confessed.    The  designation  of  the  root 
and  fifth  as  the  ''boundary  circle"  of  the  chord  is  somewhat  fanci- 
ful.    The  exact  truth  of  the  matter  eludes  our  grasp.     We  wait 
for  some  more  discerning  eye  to  detect  it.     But  the  foregoing  state- 
ment expresses  enough  truth  to  put  one  upon  the  track  of  more 
"truth  than  he  can  define  in  language,  and  however  vague  or  er- 
roneous our  explanation  of  the  matter  may  be,  the  sense  of  the  lack 
<rof  coalescence,  the  antagonism,  of  such  chords,  remains  common  to 
all. 

(E) 

Analysis  of  the  Scale-Tones,  as  Regards  the  "Leading" 

Quality. 

The  following  analysis  Is  based  upon  the  nature  of  the  several 
tones  purely  in  their  scale-relations.  From  their  relations  in  har- 
mony they  may  acquire  very  diflPerent  "leading"  qualities.  Let  the 
scale  be  played  slowly  and  attentively  several  times,  and  the  inherent 
quality  of  each  tone  in  its  scale-relation  will  be  established.  Then  let 
the  different  tones  be  struck  again,  not  in  the  order  of  their  occur- 


APPENDIX. 


257 


rence  in  the  scale,  but  as  it  were  at  random,  and  the  following  state- 
ments will  be  verified. 

The  Tonic  is  the  only  one  which  has  the  quality  of  absolute  rest 
with  no  "leading"  quality  at  all. 

The  third  and  the  fifth  approach  nearest  to  the  Tonic  in  the  qual- 
ity of  rest,  but  it  is  not  absolute.  The  third  is  not  at  all  suggestive  of 
any  tone  to  follow,  but  in  the  fifth  there  is  a  dim  foreshadowing  of 
the  Tonic. 

The  second  and  sixth  are  restless ;  somewhat  equally  poised  be- 
tween the  adjacent  tones,  but  with  the  slightly  stronger  inclination 
to  the  tone  below,  i.  e.,  the  tonic  and  dominant  respectively. 

The  fourth  has  an  evident  inclination  to  the  third. 

The  seventh  is  the  most  restless  of  all  the  tones,  and  points  em- 
phatically to  the  eighth. 

The  "leading"  quality,  in  its  increasing  force,  is  found  in  the 
foregoing  order  of  the  tones  as  follows : 


I 


3 


XE 


^^ 


5^ 


-e>- 


XE 


"cr 


As  before  remarked,  their  relations  in  the  harmony  may  entirely 
change  the  leading  quality  of  all  the  tones. 

(F) 
Reason  for  the  Two  Forms  of  the  Melodic  Minor  Scale. 


I 


XE 


XE 


Upward . 


Downward. 


iX 


m 


The  difference  is  comprised  within  the  upper  four  tones. 


I 


and  arises  from  the  preponderating  importance  of  the  "leading  tone" 
in  the  upward  scale,  and  of  the  minor  sixth  in  the  downward  scale, 
both  of  which  tones  are  essential  to  the  complete  satisfaction  of  the 
Minor  scale,  but  on  account  of  the  gap  between  them 


i 


one  is  sacrificed  to  the  other,  so  as  to  secure  a  more  melodic  pro- 


258  PARKHURST  HARMONY. 

session,  by  the  avoidance  of  an  augmented  second,  and  by  a  more 
equable  division  of  the  distance  from  E  to  G#,  and  from  A  down  to 
F,  in  having  two  successive  intervals  of  a  whole  tone  each,  rather 
than  a  half  tone  followed  by  a  tone  and  a  half,  thus : 

V      1V2  better.  i/^      iIa  better. 


i 


f 


It  remains  to  be  considered  why  the  minor  sixth  is  sacrificed  to 
the  major  seventh  in  the  upward,  and  not  in  the  downward  scale; 
and  why  the  major  seventh  is  sacrificed  to  the  minor  sixth  in  the 
downward,  and  not  in  the  upward  scale,  so  that  the  following  forms 
are  unsatisfactory: 


^^'^^   **    o   »  _  1 


if   o 


although  they  are  quite  as  melodic  as  the  same  scales  in  reverse  order. 

The  two  distinguishing  characteristics  of  the  Minor  scale  are 
the  minor  third,  and  the  minor  sixth,  and  both  of  these  intervals 
must  be  maintained  to  preserve  the  consistent  minor  quality  of  this 
scale.  But  the  stability  of  any  scale  depends  primarily  upon  main- 
taining the  pre-eminence  of  the  Tonic  of  that  scale;  and  that  pre- 
eminence is  largely  secured  by  the  emphasis  it  acquires  from  the 
tnajor  seventh  of  the  scale  in  its  leading  quality,  finding  its  "rest" 
in  the  tone  to  which  it  points,  that  is,  the  Tonic.  Therefore  when  we 
pass  from  the  seventh  to  the  eighth  we  have  impaired  the  integrity 
of  the  scale,  unless  we  find  that  emphasis  of  the  eighth  which  comes 
from  the  "leading"  quality  of  the  major  seventh,  which  helps  to  as- 
sert the  eighth  as  a  Tonic.  If  then  the  minor  sixth,  which  is  a  char- 
acteristic of  the  minor  scale,  comes  in  conflict  with  the  major 
seventh  (for  the  minor  seventh  never  "leads"),  then  the  minor  sixth 
must  be  in  a  measure  subordinated  to  the  major  seventh,  and  the 
€ar  accepts  the  major  sixth,  when  the  seventh  is  to  be  followed  by 
the  Tonic.  This  accounts  for  the  major  sixth  in  the  ascending  scale. 
But  when  the  movement  is  downward  from  the  Tonic,  and  thus  there 
is  no  demand  for  that  quality  in  the  seventh  that  shall  "lead"  to  the 
Tonic,  the  necessity  of  the  minor  sixth  outweighs  the  demand  for  a 
major  seventh,  and  the  latter  is  sacrificed  to  the  former. 

The  true  minor  scale  is  the  harmonic  form.  The  major  sixth 
and  the  minor  seventh,  that  are  found  in  the  melodic  forms,  occur 
•only  as  the  result  of  compromise.    The  various  subordinations  of  the 


APPENDIX. 


259 


sixth  to  the  seventh    and  of  the  seventh  to  the  sixtJi  are  illustrated 
in  the  following : 


ff^-f^m 


^^m 


mm 


iJP 


But  with  all  this  apparent  sacrifice  of  minor  sixth  and  of  major 
seventh,  it  is  to  be  observed  that  it  is  never  as  the  true  harmonic 
tone  that  the  major  sixth  or  the  minor  seventh  occurs,  but  only  in 
the  inconspicuous  manner  of  a  "passing"  or  "auxiliary"  tone  (see 
Chap.  XV).  The  incongruity  of  using  them  as  harmonic  tones  is 
seen  in  the  following: 

X 


'^Cf^f^US 


XE 


^ 


g 


^ 


f 


3x: 


'    1 1 ' "^ H ' "—^ — * 

The  incongruity  of  associating  the  major  sixth  and  the  minor 
third  is  plainly  felt  in  playing  the  following,  especially  if  the  two 
intervals  are  emphasized : 


i 


^ 


It  seems  inconsistent  that  the  same  incongruity  is  not  felt  in  the 
ascending  melodic  scale.  It  certainly  is  not,  and  the  reason  is 
doubtless  in  the  fact  that  in  the  upward  scale  the  gravitation  is 
strongly  toward  the  Tonic,  and  the  mind  instinctively  accepts  the 
major  sixth  as  a  temporary  compromise  to  the  "leading  tone,"  and 
lays  little  stress  upon  its  major  quality.  In  the  foregoing  downward 
scale,  however,  there  is  a  plain  assertion  of  the  A-major  scale  until 
we  reach  C,  which  as  a  minor  third,  is  a  flat  contradiction  to  A- 
major. 

(G) 
Inversion. 

The  inversion  of  a  voice  is  its  transposition  to  the  other  side  of 
an  accompanying  voice.    The  most  common  interval  of  transposition 


260 


PARKHURST  HARMONY. 


is  the  octave,  but  any  other  interval  can  also  be  used.  In  all  the 
following  illustrations,  the  octave  (which  means  one,  two  or  any 
number  of  octaves)  is  the  interval  of  transposition,  unless  other- 
wise specified. 

The  following  shows  the  inversion  of  the  lower  voice  above  the 
upper,  and  of  the  upper  below  the  lower : 


s 


^ 


l"\'  Hi;/" 


XX 


o\o 


It  will  be  seen  that  the  resulting  interval  between  the  voices 
is  the  same,  whether  the  lower  or  the  upper  voice  be  inverted. 

The  following  shows  the  result  of  inverting  the  upper  or  the 
lower  of  two  voices  standing  at  the  successive  intervals  of  the  dia- 
tonic scale : 


3 


AW^>)       .Al^)       yW 


5 


'F=^ 


^ 


£1. 


^ 


)         fM^Mmt 


(K       (o^>     t^**» 


XE 


6 


"CT" 

7 


6 


The  original  and  resulting  intervals  are  expressed  by  the  follow- 
ing series  of  numbers : 

12345678 
87654321 

thus  a  prime  becomes  an  octave;  a  second  becomes  a  seventh;  a 
third  a  sixth,  etc.,  and  the  sum  of  the  original  and  inverted  inter- 
vals is  always  9.  Thus  the  larger  the  original  interval,  the  smaller 
will  be  the  inverted  interval,  and  vice  versa;  also  the  larger  size  of 
one  interval  inverts  into  the  smaller  size  of  the  other ;  hence  a  major 
interval  inverts  into  a  minor,  and  a  minor  into  a  major,  and  a  di- 
minished into  an  augmented. 

Major  into  Minor,  and  vice  versa. 


minor. 
,7 


maior.    mmor.  ^"^j^i-    *"*"ui. 
,    n^ajor.    minor,  n^a^r.    minor.       ^^     ^^^       L  ^     \.L  ^ 

minor,  maior.    minor,    major,    minor.- maior. 'minQr,  majot^ 


«5 ^fT" 

7  7 

minor,  major. 


6 

major 


APPENDIX. 


261 


Augmented  into  Diminished^  and  vice  versa. 


I 


aug. 
i 


^ 


"I 


2 


i 


8 
dim. 


4 


aug. 
5 


15 — 

dim. 

diin. 
5 


dim. 

(.3  , 


^ 


aug. 


6 

aug. 


^ 


o: 


dim. 
4 


XE 


5 

dim. 

dim. 


5 

aug. 

dim. 


tf'ci'    htf»^^    I  (tf"!^^  I  '■g**'^^^  j 


4 
dim 


4 
aug. 


3 
dim. 


aug. 


T 

aug. 


It  is  evident  that  unless  the  two  voices  are  within  an  octave  of 
each  other,  the  transposition  of  either  of  them  by  a  single  octave  will 
not  result  in  an  inversion : 


4   °f   "■!    °-f    I 

t)    -o       ^       ^^ 


thus  a  ninth  becomes  a  second;  a  tenth,  a  third,  etc.,  and  the  result- 
ing interval  is  essentially  the  same.  But  if  the  voice  be  transposed 
two  or  more  octaves,  an  inversion  is  secured,  and  the  resulting  inter- 
vals are  either  identically  or  essentially  the  same  as  when  either  of 
the  voices,  within  the  limits  of  an  octave  from  the  other,  is  trans- 
posed a  single  octave ;  thus : 

Transposed     Transposed       Transposed 
one  octave,    two  octaves,    three  octaves. 


In  all  the  above  inversions  the  upper  intervals  are  either  abso- 
lutely or  essentially  thirds,  and  the  lower  intervals  are  either  abso- 
lutely or  essentially  sixths.  So  that  what  may  be  called  the  octave 
inversion  invariably  produces  such  an  interval  as,  in  its  relation  to 
the  original  interval,  is  expressed  by  the  same  number  as  if  the  voices 
were  within  an  octave,  and  inverted  by  an  octave. 

The  ociave  does  not  invariably  become  a  prime  by  inversion,  but 
the  prime  always  inverts  to  the  octave  (one  or  more  octaves).  The 
octave  may  invert  to  an  octave ;  thus : 


262 


PARKHURST  HARMONY. 


octave  to 
prime. 


prime  to 
octave . 


The  transposition  from  octave  to  unison,  and  from  unison  to 
octave,  necessarily  ranks  as  an  inversion,  yet  without  being  a  transfer 
from  one  side  to  the  other,  and  is  devoid  of  that  essential  harmonic 
change  of  relation  between  the  voices  that  results  from  all  the  other 
inversions. 

Besides  the  octave-inversion,  it  is  possible  to  invert  by  any  other 
interval,  either  less  or  greater  than  the  octave.  Of  all  other  in- 
versions the  commonest  in  use  are  the  inversions  of  the  tenth  and 
the  twelfth,  thus : 


inversion  6f  the  tenth. 

inversion  df  the  twelfth. 

-if                                                      ^-fc  «»  , 

_^      4«     O     *' 

n                                 r»    **   ^ 

r^   *»     " 

Tm                   r*   •»    ^^ 

c^    *»     ^^ 

vV     r»    ** 

^      -^  -€^  -O- -O-  -O-  -«--€> -»► 

-O-  -^  -€^-^    -O-  -^  -^  -^ 

h-r^.                                ^     «»     *> 

<-»     **     •^ 

r^     *»   *^ 

-■•^ 

«»    *^                                             ■    

The  explanation  of  inversion  properly  belongs  to  the  subject  of 
Harmony  as  it  relates  to  certain  harmonic  relations  of  tones;  but  the 
application  of  inversion  belongs  only  to  the  higher  forms  of  musical 
composition.  Yet  as  a  matter  of  interest  to  the  student,  and  to  give 
him  a  better  understanding  of  the  subject,  the  use  of  inversion  will 
be  briefly  explained. 

Suppose  we  have  a  short  melodic  phrase  in  one  voice,  like  the 
following : 


i 


^^^ 


Xfl 


^ 


-o- 


to  which  we  wish  to  add  an  accompanying  voice,  thus : 


'^WW'f"'''^^'' -'^'r 


If  this  accompanying  part  be  written  according  to  certain  laws 
that  pertain  to  this  sort  of  composition,  it  can  serve  not  only  to  ac- 
company the  first  voice  in  its  present  position,  but  also  if  one  or  the 
other  of  the  two  voices  be  inverted  throughout  by  an  octave,  thus: 


APPENDIX. 


263 


this  secures  new  harmonic  effects  throughout,  while  the  voices  them- 
selves are  identically  the  same.  This  is  one  of  the  arts  of  the  com- 
poser for  gaining  nezv  effects  with  old  material;  that  is,  securing 
unity  and  variety,  th^  two  fundamental  requisites  of  every  com- 
lX)sition. 

The  foregoing  sufficiently  explains  the  purpose  of  inversion, 
whether  by  the  octave,  which  is  the  most  common,  or  by  any  other 
interval. 

(H) 

The  Tdextitv  axd  the  Difference  of  Aug^iexted  Sixth 
AND  Minor  Seventh. 

chord  of  aug. sixth,      chord  of  dominant 
a^g. sixth. minor  seventh,  wiih  resolution,  seventh, with  resolution, 

i: 


avg.sixin 


t 


3z: 


XE 


izxz: 


#» 


s 


m 


xn 


o: 


s 


I 


chord  of  aug.  sixth  and 
fifth, with  resolution. 


chord  of  dominant 
;eyenth,with  resolution. 


i 


I 


*8 


CE 


€>- 


B 


-v^ — 

The  ear  knows  nothing  of  sharps,  flats,  or  naturals.  These  si^iis 
are  simply  devices  of  Notation,  so  as  to  express  precisely  to  the  eye 
the  relation  and  interval  of  tones,  as  the  relation  and  interval  exist  to 
the  ear.  What  we  may  call  the  physical  distance  of  D#  from  F 
(as  above)  is  precisely  the  same  (for  all  practical  purposes)  as  the 
distance  of  Eb  from  F.  But  under  some  circumstances  the  ear  rec- 
ognizes this  interval  as  an  augmented  sixth,  and  under  other  circum- 
stances as  a  minor  seventh,  and  according  as  it  is  felt  to  be  the  one 
or  the  other,  the  following  progression  is  thereby  determined.  This 
progression  differs  radically  in  the  two  cases,  for  it  is  in  the  nature 
of  an  augmented  sixth  to  lead  up  a  miiior  second  (i.  e.,  a  semitone), 
and  it  is  in  the  nature  of  every  seventh  to  lead  doz^'u  one  degree 
(which  may  be  either  a  major  or  a  minor  second). 

The  normal  resolution  of  all  discords  may  he  said  to  b?  down- 
ward, however  inexplicable  the  fact  may  be.  This  is  amply  illus- 
trated in  the  *'sus})ension-chords,"  wherein  one  sees  the  constant 
drawing  of  the  ninth  down  to  the  eighth,  of  the  sixth  to  the  fifth,  of 
the  fourth  to  the  third,  and.  in  the  commonest  of  all  discords,  of  the 


264 


PARKHURST  HARMONY. 


seventh  to  the  sixth.  A  strong  counterbalancing  consideration  must 
therefore  exist  in  that  interval  which  would  ordinarily  be  regarded 
as  a  minor  seventh,  neutralizing  the  natural  tendency,  and  leading 
from  the  discordant  tone  upward;  in  which  circumstance  the  interval 
is  felt  to  be  a  sixth  (of  the  augmented  sort),  rather  than  a  seventh. 

The  exceptional  treatment  of  this  discord  is  explained  by  saying, 
that  the  mind  constantly  recognizes  the  fact  that  the  coherence  and 
musical  sense  of  successive  chords  depend  largely  upon  their  Hoiving 
in  one  and  the  same  scale,  or  only  from  one  scale  to  another  wherein 
the  modulation  shall  not  sever  the  coherence. 

In  the  following  progression  the  chords  cohere  in  the  same  scale, 
when  the  discordant  D#  leads  up  to  E. 


J 


m 


xy 


t 


£J[|-|,iU 


g 


^ 

-^ 


« 


6  -e- 


a 


\^ 


The  same  discord,  regarded  as  a  seventh,  involves  in  its  natural 
resolution  a  chord  that  is  out  of  all  coherence  with  the  preceding 
chords,  and  necessitates  a  modulation  that  is  utterly  forced  and  un- 
natural. 


^ 


iti 


-t> 


i 


m 


-« ; 


<^ 


6      1.7 

If  the  passage  were  in  the  key  of  Bb,  it  would  be  equally  incom- 
patible with  the  scale  to  lead  up  from  the  discordant  tone,  as  at 
(a),  which  would  now  be  construed  as  a  seventh,  and  resolve  as 
at  (b). 

X 


^ 


2 


m 


XX. 


APPENDIX. 


265 


To  state  the  matter  briefly,  the  foregoing  discord  is  naturally  re- 
garded as  a  minor  seventh,  but  wherever  such  interpretation  leads 
to  an  incoherence  of  the  chords,  and  to  a  forced  modulation,  the  mind 
construes  the  discord  as  a  sixth  (of  the  augmented  sort).  A  cir- 
cumstance which  often  makes  it  easier  to  construe  this  as  an  aug- 
mented sixth  is  the  fact  that  the  melody  frequently  leads  up  to  it,  and 
what  we  may  call  a  melodic  momentum  in  a  measure  predetermines 
the  upward  resolution. 

This  is  only  one  instance  of  the  mental  process  of  determining 
the  nature  of  an  interval  according  to  the  situation  in  which  it  occurs. 
Thus  the  interval  which  under  some  circumstances  is  a  major  second, 
under  others  is  a  diminished  third;  what  is  sometimes  an  augmented 
second  is  at  other  times  a  minor  third;  what  is  sometimes  a  major 
third  is  at  other  times  a  diminished  fourth,  etc.  The  following  table 
presents  the  various  equivalent  intervals. 


I 


diminished 
major  second.  third. 


ir 


aug^.  second.      minor  third. 


^^ 


s 


\>\>K>^ 


^ 


O- 


diminished  '  '  diminished    ^ 

major  third.  fourth.  aug.  fourth.  fifth. 


1^ 


* 


€>- 


IE 


'    aug.  fifth. 


mino 


r  sixth.      ' '       aug.  sixth. 


^ 


a: 


t 


minor  seventh.  major* seventh.       diminished  eighth. 


^ 


EE 


-fJT 


(I) 

The  Essential  Principle  of  Notation. 

The  chapter  on  "altered  chords"  brings  to  our  notice  certain  in- 
tervals that  are  ambiguous,  i.e.,  dependent  upon  circumstances  to 
determine  their  name.  Thus  the  distance  which  in  some  cases  is  an 
augmented  fifth,  is  in  other  cases  a  minor  sixth.  The  distance  of  an 
augmented  sixth  is  often  a  minor  seventh.  (For  a  full  list  of  the 
equivalent,  and  therefore  ambiguous  intervals,  see  Appendix  (H)  ). 
The  question  is  often  asked,  why  a  given  interval  is  expressed  in  no- 
tation as  it  is,  and  the  answer  commonly  given  is,  ''to  conform  to  the 


266 


PARKHURST  HARMONY. 


principles  of  Notation;"  which  leaves  the  enquirer  no  wiser  than 
before,  but  inspires  within  him  a  proper  awe  in  view  of  the  mysteri- 
ous "principles  of  Notation."  There  is  but  one  essential  principle 
of  Notation,  and  that  a  simple  one,  viz.,  to  express  the  relations  of 
tones  to  the  eye  exactly  as  they  exist  to  the  ear.  In  determining 
intervals  between  tones,  the  ear  moves  along  the  steps  of  the  diatonic 
scale.  These  steps  of  the  scale  are  expressed  to  the  eye  by  the  lines 
and  spaces  of  the  staff,  and  there  must  be  as  many  intervening  lines 
and  spaces  as  there  are  intervening  steps  of  the  scale.  To  illustrate 
this,  suppose  two  tones  are  heard,  which  we  will  call  C — F#, 

«    3      4 


I 


* 


and  supposing  the  scale  of  G  to  be  already  established  in  the  mind, 
the  ear  moves  in  that  scale  through  tones  which  we  call  D  and  E, 
so  that  the  interval  is  expressed  in  notation,  c — d — e — f#,  a  fourth. 
But  again,  supposing  the  scale  of  Db  to  be  already  in  the  mind,  then 
the  ear  will  move  in  that  scale,  and  the  interval  is  expressed  in  notation 
thus,  c — db — eb — f — gb,  a  iifth. 

3     4 


tl        2       3     4 


This  illustrates  the  one  essential  principle  of  Notation.  The  real 
relation  is  that  which  the  ear  hears,  and  the  notation  is  accurate 
when  the  eye  sees  as  the  ear  hears. 


14  DAY  USE 

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